SCIENTIFIC  LECTURES 


UCSB   LIBRARf 


POPULAR  SCIENTIFIC  LECTURES. 


BY  THE  SAME  AUTHOR. 


THE  SCIENCE  OF  MECHANICS.  Translated  from  the 
Second  German  Edition  by  T.  J.  McCormack. 
250  Cuts  and  Illustrations.  534  Pages.  Half 
Morocco,  Gilt  Top.  Price,  $2.50. 

CONTRIBUTIONS  TO  THE  ANALYSIS  OF  THE  SENSATIONS. 
Translated  by  C.  M.  Williams.  With  Notes  and 
New  Additions  by  the  Author.  200  Pages.  36 
Cuts.  Price,  $1.00. 

POPULAR  SCIENTIFIC  LECTURES.  Translated  by  T. 
J.  McCormack.  Third  Revised  and  Enlarged 
Edition.  411  Pages.  59  Cuts.  Cloth,  $1.50; 
Paper,  50  cents. 


THE   OPEN   COURT   PUBLISHING   CO., 

324  DEARBORN  ST.,  CHICAGO. 


POPULAR 

SCIENTIFIC  LECTURES 


ERNST  MACH 


FORMERLY  PROFESSOR  OF  PHYSICS  IN  THE  UNIVERSITY  OF  PRAGUE,  NOW 

PROFESSOR  OF  THE  HISTORY  AND  THEORY  OF  INDUCTIVE 

SCIENCE  IN  THE  UNIVERSITY  OF  VIENNA 


TRANSLATED 

BY 

THOMAS  J.  McCORMACK 


THIRD  EDITION,  REVISED  AND  ENLARGED 


WITH  FIFTY-NINE  CUTS  AND  DIAGRAMS 


CHICAGO 

THE  OPEN  COURT  PUBLISHING  COMPANY 

FOR  SALE  DY 

KEGAN  PAUL,  TRENCH,  TRUEBNER  &  Co.,  LONDON 
1898 


COPYRIGHT 
BY  THE  OPEN  COURT  PUBLISHING  Co. 


Pages      1-258  I  -      g 
Pages  338-374  f 
Pages  259-281  in  1896. 
Pages  282-308  m  1897. 
Pages  309-337  in  1898. 


AUTHOR'S   PREFACE  TO  THE   FIRST 
EDITION. 


T~)OPULAR  LECTURES,  owing  to  the  knowledge  they  presup- 
JL  pose,  and  the  time  they  occupy,  can  afford  only  a  modicum 
of  instruction.  They  must  select  for  this  purpose  easy  subjects, 
and  restrict  themselves  to  the  exposition  of  the  simplest  and  the 
most  essential  points.  Nevertheless,  by  an  appropriate  choice  of 
the  matter,  the  charm  and  the  poetry  of  research  can  be  conveyed 
by  them.  It  is  only  necessary  to  set  forth  the  attractive  and  the 
alluring  features  of  a  problem,  and  to  show  what  broad  domains 
of  fact  can  be  illuminated  by  the  light  radiating  from  the  solution 
of  a  single  and  ofttimes  unobtrusive  point. 

Furthermore,  such  lectures  can  exercise  a  favorable  influence 
by  showing  the  substantial  sameness  of  scientific  and  every-day 
thought.  The  public,  in  this  way,  loses  its  shyness  towards  scien- 
tific questions,  and  acquires  an  interest  in  scientific  work  which  is 
a  great  help  to  the  inquirer.  The  latter,  in  his  turn,  is  brought  to 
understand  that  his  work  is  a  small  part  only  of  the  universal  pro- 
cess of  life,  and  that  the  results  of  his  labors  must  redound  to  the 
benefit  not  only  of  himself  and  a  few  of  his  associates,  but  to  that 
of  the  collective  whole. 

I  sincerely  hope  that  these  lectures,  in  the  present  excellent 
translation,  will  be  productive  of  good  in  the  direction  indicated. 

E.  MACH. 
PRAGUE,  December,   1894. 


TRANSLATOR'S  NOTE  TO  THE 
THIRD  EDITION. 


THE  present  third  edition  of  this  work  has  been  enlarged  by 
the  addition  of  a  new  lecture,  "  On  Some  Phenomena  At- 
tending the  Flight  of  Projectiles."  The  additions  to  the  second 
consisted  of  the  following  four  lectures  and  articles  :  Professor 
Mach's  Vienna  Inaugural  Lecture,  "The  Part  Played  by  Accident 
in  Invention  and  Discovery,"  the  lecture  on  "  Sensations  of  Orien- 
tation," recently  delivered  and  summing  up  the  results  of  an  im- 
portant psychological  investigation,  and  two  historical  articles  (see 
Appendix)  on  Acoustics  and  Sight. 

The  lectures  extend  over  a  long  period,  from  1864  to  1898, 
and  differ  greatly  in  style,  contents,  and  purpose.  They  were  first 
published  in  collected  form  in  English  ;  afterwards  two  German 
editions  were  called  for. 

As  the  dates  of  the  first  five  lectures  are  not  given  in  the  foot- 
notes they  are  here  appended.  The  first  lecture,  "  On  the  Forms 
of  Liquids,"  was  delivered  in  1868  and  published  with  that  "On 
Symmetry  "  in  1872  (Prague).  The  second  and  third  lectures,  on 
acoustics,  were  first  published  in  1865  (Graz);  the  fourth  and  fifth, 
on  optics,  in  1867  (Graz).  They  belong  to  the  earliest  period  of 
Professor  Mach's  scientific  activity,  and  with  the  lectures  on  electro- 
statics and  education  will  more  than  realise  the  hope  expressed  in 
the  author's  Preface. 

The  eighth,  ninth,  tenth,  eleventh,  and  twelfth  lectures  are  of 


viii  TRANSLA  TORS  NO  TE. 

a  more  philosophical  character  and  deal  principally  with  the  meth- 
ods and  nature  of  scientific  inquiry.  In  the  ideas  summarised  in 
them  will  be  found  one  of  the  most  important  contributions  to  the 
theory  of  knowledge  made  in  the  last  quarter  of  a  century.  Sig- 
nificant hints  in  psychological  method,  and  exemplary  specimen- 
researches  in  psychology  and  physics,  are  also  presented  ;  while  in 
physics  many  ideas  find  their  first  discussion  that  afterwards,  under 
other  names  and  other  authorship,  became  rallying-cries  in  this 
department  of  inquiry. 

All  the  proofs  of  this  translation  have  been  read  by  Professor 
Mach  himself. 

T.  J.   McCORMACK. 

LA  SALLE,  ILL.,  May,  1898. 


TABLE  OF  CONTENTS. 


The  Forms  of  Liquids i 

The  Fibres  of  Corti 17 

On  the  Causes  of  Harmony 32 

The  Velocity  of  Light 48 

Why  Has  Man  Two  Eyes  ? 66 

On  Symmetry 89 

On  the  Fundamental  Concepts  of  Electrostatics 107 

On  the  Principle  of  the  Conservation  of  Energy 137 

On  the  Economical  Nature  of  Physical  Inquiry 186 

On  Transformation  and  Adaptation  in  Scientific  Thought  .     .214 

On  the  Principle  of  Comparison  in  Physics 236 

On  the  Part  Played  by  Accident  in  Invention  and  Discovery  .  259 

On  Sensations  of  Orientation 282 

On  Some  Phenomena  Attending  the  Flight  of  Projectiles    .     .  309 
On  Instruction  in  the  Classics  and  the  Mathematico-Physical 

Sciences 338 

Appendixes. 

I.  A  Contribution  to  the  History  of  Acoustics     ....  375 

II.  Remarks  on  the  Theory  of  Spatial  Vision 386 

Index 393 


THE  FORMS  OF  LIQUIDS. 


WHAT  thinkest  thou,  dear  Euthyphron,  that  the 
holy  is,  and  the  just,  and  the  good  ?  Is  the  holy 
holy  because  the  gods  love  it,  or  are  the  gods  holy  be- 
cause they  love  the  holy  ?  By  such  easy  questions  did 
the  wise  Socrates  make  the  market-place  of  Athens  un- 
safe and  relieve  presumptuous  young  statesmen  of  the 
burden  of  imaginary  knowledge,  by  showing  them  how 
confused,  unclear,  and  self-contradictory  their  ideas 
were. 

You  know  the  fate  of  the  importunate  questioner. 
So  called  good  society  avoided  him  on  the  promenade. 
Only  the  ignorant  accompanied  him.  And  finally  he 
drank  the  cup  of  hemlock — a  lot  which  we  ofttimes 
wish  would  fall  to  modern  critics  of  his  stamp. 

What  we  have  learned  from  Socrates,  however, — 
our  inheritance  from  him,  —  is  scientific  criticism. 
Every  one  who  busies  himself  with  science  recognises 
how  unsettled  and  indefinite  the  notions  are  which  he 
has  brought  with  him  from  common  life,  and  how,  on 
a  minute  examination  of  things,  old  differences  are 


2  THE  FORMS  OF  LIQUIDS. 

effaced  and  new  ones  introduced.  The  history  of  sci- 
ence is  full  of  examples  of  this  constant  change,  de- 
velopment, and  clarification  of  ideas. 

But  we  will  not  linger  by  this  general  consideration 
of  the  fluctuating  character  of  ideas,  which  becomes  a 
source  of  real  uncomfortableness,  when  we  reflect  that 
it  applies  to  almost  every  notion  of  life.  Rather  shall 
we  observe  by  the  study  of  a  physical  example  how 
much  a  thing  changes  when  it  is  closely  examined,  and 
how  it  assumes,  when  thus  considered,  increasing  defi- 
niteness  of  form. 

The  majority  of  you  think,  perhaps,  you  know 
quite  well  the  distinction  between  a  liquid  and  a  solid. 
And  precisely  persons  who  have  never  busied  them- 
selves with  physics  will  consider  this  question  one  of 
the  easiest  that  can  be  put.  But  the  physicist  knows 
that  it  is  one  of  the  most  difficult.  I  shall  mention 
here  only  the  experiments  of  Tresca,  which  show  that 
solids  subjected  to  high  pressures  behave  exactly  as 
liquids  do ;  for  example,  may  be  made  to  flow  out  in 
the  form  of  jets  from  orifices  in  the  bottoms  of  vessels. 
The  supposed  difference  of  kind  between  liquids  and 
solids  is  thus  shown  to  be  a  mere  difference  of  degree. 

The  common  inference  that  because  the  earth  is 
oblate  in  form,  it  was  originally  fluid,  is  an  error,  in 
the  light  of  these  facts.  True,  a  rotating  sphere,  a  few 
inches  in  diameter  will  assume  an  oblate  form  only 
if  it  is  very  soft,  for  example,  is  composed  of  freshly 
kneaded  clay  or  some  viscous  stuff.  But  the  earth, 


THE  FORMS  OF  LIQUIDS.  3 

even  if  it  consisted  of  the  rigidest  stone,  could  not 
help  being  crushed  by  its  tremendous  weight,  and  must 
perforce  behave  as  a  fluid.  Even  our  mountains  could 
not  extend  beyond  a  certain  height  without  crumbling. 
The  earth  may  once  have  been  fluid,  but  this  by  no 
means  follows  from  its  oblateness. 

The  particles  of  a  liquid  are  displaced  on  the  ap- 
plication of  the  slightest  pressure  ;  a  liquid  conforms 
exactly  to  the  shapes  of  the  vessels  in  which  it  is  con- 
tained ;  it  possesses  no  form  of  its  own,  as  you  have 
all  learned  in  the  schools.  Accommodating  itself  in 
the  most  trifling  respects  to  the  conditions  of  the  vessel 
in  which  it  is  placed,  and  showing,  even  on  its  surface, 
where  one  would  suppose  it  had  the  freest  play,  nothing 
but  a  polished,  smiling,  expressionless  countenance, 
it  is  the  courtier  par  excellence  of  the  natural  bodies. 

Liquids  have  no  form  of  their  own  !  No,  not  for  the 
superficial  observer.  But  persons  who  have  observed 
that  a  raindrop  is  round  and  never  angular,  will  not  be 
disposed  to  accept  this  dogma  so  unconditionally. 

It  is  fair  to  suppose  that  every  man,  even  the  weak- 
est, would  possess  a  character,  if  it  were  not  too  diffi- 
cult in  this  world  to  keep  it.  So,  too,  we  must  sup- 
pose that  liquids  would  possess  forms  of  their  own,  if 
the  pressure  of  the  circumstances  permitted  it, — if 
they  were  not  crushed  by  their  own  weights. 

An  astronomer  once  calculated  that  human  beings 
could  not  exist  on  the  sun,  apart  from  its  great  heat, 
because  they  would  be  crushed  to  pieces  there  by  their 


4  THE  FORMS  OF  LIQUIDS. 

own  weight.  The  greater  mass  of  this  body  would 
also  make  the  weight  of  the  human  body  there  much 
greater.  But  on  the  moon,  because  here  we  should 
be  much  lighter,  we  could  jump  as  high  as  the  church- 
steeples  without  any  difficulty,  with  the  same  muscular 
power  which  we  now  possess.  Statues  and  "plaster" 
casts  of  syrup  are  undoubtedly  things  of  fancy,  even 
on  the  moon,  but  maple-syrup  would  flow  so  slowly 
there  that  we  could  easily  build  a  maple-syrup  man  on 
the  moon,  for  the  fun  of  the  thing,  just  as  our  children 
here  build  snow-men. 

Accordingly,  if  liquids  have  no  form  of  their  own 
with  us  on  earth,  they  have,  perhaps,  a  form  of  their 
own  on  the  moon,  or  on  some  smaller  and  lighter  heav- 
enly body.  The  problem,  then,  simply  is  to  get  rid  of 
the  effects  of  gravity ;  and,  this  done,  we  shall  be  able 
to  find  out  what  the  peculiar  forms  of  liquids  are. 

The  problem  was  solved  by  Plateau  of  Ghent,  whose 
method  was  to  immerse  the  liquid  in  another  of  the 
same  specific  gravity.*  He  employed  for  his  experi- 
ments oil  and  a  mixture  of  alcohol  and  water.  By 
Archimedes's  well-known  principle,  the  oil  in  this  mix- 
ture loses  its  entire  weight.  It  no  longer  sinks  be- 
neath its  weight ;  its  formative  forces,  be  they  ever  so 
weak,  are  now  in  full  play. 

As  a  fact,  we  now  see,  to  our  surprise,  that  the  oil, 
instead  of  spreading  out  into  a  layer,  or  lying  in  a 


*  Statique  expirimentale  et  thlorique  des  liquides,  1873.     See  also  The  Sci- 
ence of  Mechanics,  p.  384  et  seqq.,The  Open  Court  Publishing  Co.,  Chicago,  1893. 


THE  FORMS  OF  LIQUIDS. 


formless  mass,  assumes  the  shape  of  a  beautiful  and 
perfect  sphere,  freely  suspended  in  the  mixture,  as 
the  moon  is  in  space.  We  can  construct  in  this  way  a 
sphere  of  oil  several  inches  in  diameter. 

If,  now,  we  affix  a  thin  plate  to  a 
wire  and  insert  the  plate  in  the  oil 
sphere,  we  can,  by  twisting  the  wire 
between  our  fingers,  set  the  whole  ball 
in  rotation.  Doing  this,  the  ball  as- 
sumes an  oblate  shape,  and  we  can,  if 
we  are  skilful  enough,  separate  by  such 
rotation  a  ring  from  the  ball,  like  that 
which  surrounds  Saturn.  This  ring  is 
finally  rent  asunder,  and,  breaking  up 
into  a  number  of  smaller  balls,  exhibits 
to  us  a  kind  of  model  of  the  origin  of 
the  planetary  system  according  to  the 
hypothesis  of  Kant  and  Laplace. 

Still  more  curious  are  the  phe- 
nomena exhibited  when  the  formative 
forces  of  the  liquid  are  partly  disturbed 
by  putting  in  contact  with  the  liquid's 
surface  some  rigid  body.  If  we  im- 
merse, for  example,  the  wire  framework  of  a  cube  in  our 
mass  of  oil,  the  oil  will  everywhere  stick  to  the  wire 
framework.  If  the  quantity  of  oil  is  exactly  sufficient 
we  shall  obtain  an  oil  cube  with  perfectly  smooth  walls. 
If  there  is  too  much  or  too  little  oil,  the  walls  of  the 
cube  will  bulge  out  or  cave  in.  In  this  manner  we 


Fig.  i. 


THE  FORMS  OF  LIQUIDS. 


can  produce  all  kinds  of  geometrical  figures  of  oil,  for 
example,  a  three-sided  pyramid,  a  cylinder  (by  bring- 
ing the  oil  between  two  wire  rings),  and  so  on.  In- 
teresting is  the  change  of  form  that  occurs  when  we 
gradually  suck  out  the  oil  by  means  of  a  glass  tube 
from  the  cube  or  pyramid.  The  wire  holds  the  oil 
fast.  The  figure  grows  smaller  and  smaller,  until  it  is 
at  last  quite  thin.  Ultimately  it  consists  simply  of  a 


Fig.  2. 

number  of  thin,  smooth  plates  of  oil,  which  extend 
from  the  edges  of  the  cube  to  the  centre,  where  they 
meet  in  a  small  drop.  The  same  is  true  of  the  pyramid. 
The  idea  now  suggests  itself  that  liquid  figures  as 
thin  as  this,  and  possessing,  therefore,  so  slight  a 
weight,  cannot  be  crushed  or  deformed  by  their  weight ; 
just  as  a  small,  soft  ball  of  clay  is  not  affected  in  this 
respect  by  its  weight.  This  being  the  case,  we  no 
longer  need  our  mixture  of  alcohol  and  water  for  the 
production  of  figures,  but  can  construct  them  in  the 


THE  FORMS  OF  LIQUIDS.  7 

open  air.  And  Plateau,  in  fact,  found  that  these  thin 
figures,  or  at  least  very  similar  ones,  could  be  pro- 
duced in  the  air,  by  dipping  the  wire  nets  described 
in  a  solution  of  soap  and  water  and  quickly  drawing 
them  out  again.  The  experiment  is  not  difficult.  The 
figure  is  formed  of  itself.  The  preceding  drawing 
represents  to  the  eye  the  forms  obtained  with  cubical 
and  pyramidal  nets.  In  the  cube,  thin,  smooth  films 
of  soap-suds  proceed  from  the  edges  to  a  small,  quad- 
ratic film  in  the  centre.  In  the  pyramid,  a  film  pro- 
ceeds from  each  edge  to  the  centre. 

These  figures  are  so  beautiful  that  they  hardly  ad- 
mit of  appropriate  description.  Their  great  regularity 
and  geometrical  exactness  evokes  surprise  from  all  who 
see  them  for  the  first  time.  Unfortunately,  they  are  of 
only  short  duration.  They  burst,  on  the  drying  of  the 
solution  in  the  air,  but  only  after  exhibiting  to  us  the 
most  brilliant  play  of  colors,  such  as  is  often  seen  in 
soap-bubbles.  Partly  their  beauty  of  form  and  partly 
our  desire  to  examine  them  more  minutely  induces  us 
to  conceive  of  methods  of  endowing  them  with  perma- 
nent form.  This  is  very  simply  done.*  Instead  of 
dipping  the  wire  nets  in  solutions  of  soap,  we  dip  them 
in  pure  melted  colophonium  (resin).  When  drawn 
out  the  figure  at  once  forms  and  solidifies  by  contact 
with  the  air. 

It  is  to  be  remarked  that  also  solid  fluid-figures  can 


*  Compare  Mach,  Utbtr  die  Moleculanvirkitng  der  Fliissiskeiten,  Reports 
of  the  Vienna  Academy,  1862. 


8  THE  FORMS  OF  LIQUIDS. 

be  constructed  in  the  open  air,  if  their  weight  be  light 
enough,  or  the  wire  nets  of  very  small  dimensions.  If 
we  make,  for  example,  of  very  fine  wire  a  cubical  net 
whose  sides  measure  about  one-eighth  of  an  inch  in 
length,  we  need  simply  to  dip  this  net  in  water  to  ob- 
tain a  small  solid  cube  of  water.  With  a  piece  of  blot- 
ting paper  the  superfluous  water  may  be  easily  removed 
and  the  sides  of  the  cube  made  smooth. 

Yet  another  simple  method  may  be  devised  for  ob- 
serving these  figures.  A  drop  of  water  on  a  greased 
glass  plate  will  not  run  if  it  is  small  enough,  but  will  j- 
be  flattened  by  its  weight,  which  presses  it  against 
its  support.  The  smaller  the  drop  the  less  the  flatten- 
ing. The  smaller  the  drop  the  nearer  it  approaches 
the  form  of  a  sphere.  On  the  other  hand,  a  drop  sus- 
pended from  a  stick  is  elongated  by  its  weight.  The 
undermost  parts  of  a  drop  of  water  on  a  support  are 
pressed  against  the  support,  and  the  upper  parts  are 
pressed  against  the  lower  parts  because  the  latter  can- 
not yield.  But  when  a  drop  falls  freely  downward 
all  its  parts  move  equally  fast ;  no  part  is  impeded  by 
another ;  no  part  presses  against  another.  A  freely 
falling  drop,  accordingly,  is  not  affected  by  its  weight ; 
it  acts  as  if  it  were  weightless ;  it  assumes  a  spherical 
form. 

A  moment's  glance  at  the  soap-film  figures  pro- 
duced by  our  various  wire  models,  reveals  to  us  a  great 
multiplicity  of  form.  But  great  as  this  multiplicity  is, 


THE  FORMS  OF  LIQUIDS.  g 

the  common  features  of  the  figures  also  are  easily  dis- 
cernible. 

14  All  forms  of  Nature  are  allied,  though  none  is  the  same  as  the  other; 
Thus,  their  common  chorus  points  to  a  hidden  law." 

This  hidden  law  Plateau  discovered.  It  may  be 
expressed,  somewhat  prosily,  as  follows  : 

1)  If  several  plane  liquid  films  meet  in  a  figure 
they  are  always  three  in  number,  and,  taken  in  pairs, 
form,  each  with  another,  nearly  equal  angles. 

2)  If  several  liquid  edges  meet  in  a  figure  they  are 
always  four  in  number,  and,  taken  in  pairs,  form,  each 
with  another,  nearly  equal  angles. 

This  is  a  strange  law,  and  its  reason  is  not  evident. 
But  we  might  apply  this  criticism  to  almost  all  laws. 
It  is  not  always  that  the  motives  of  a  law-maker  are 
discernible  in  the  form  of  the  law  he  constructs.  But 
our  law  admits  of  analysis  into  very  simple  elements 
or  reasons.  If  we  closely  examine  the  paragraphs 
which  state  it,  we  shall  find  that  their  meaning  is  simply 
this,  that  the  surface  of  the  liquid  assumes  the  shape 
of  smallest  area  that  is  possible  under  the  circum- 
stances. 

If,  therefore,  some  extraordinarily  intelligent  tailor, 
possessing  a  knowledge  of  all  the  artifices  of  the  higher 
mathematics,  should  set  himself  the  task  of  so  cover- 
ing the  wire  frame  of  a  cube  with  cloth  that  every  piece 
of  cloth  should  be  connected  with  the  wire  and  joined 
with  the  remaining  cloth,  and  should  seek  to  accom- 
plish this  feat  with  the  greatest  saving  of  material,  he 


io  THE  FORMS  OF  LIQUIDS. 

would  construct  no  other  figure  than  that  which  is  here 
formed  on  the  wire  frame  in  our  solution  of  soap  and 
water.  Nature  acts  in  the  construction  of  liquid  figures 
on  the  principle  of  a  covetous  tailor,  and  gives  no 
thought  in  her  work  to  the  fashions.  But,  strange  to 
say,  in  this  work,  the  most  beautiful  fashions  are 
of  themselves  produced. 

The  two  paragraphs  which  state  our  law  apply  pri- 
marily only  to  soap-film  figures,  and  are  not  applicable, 
of  course,  to  solid  oil-figures.  But  the  principle  that 
the  superficial  area  of  the  liquid  shall  be  the  least 
possible  under  the  circumstances,  is  applicable  to  all 
fluid  figures.  He  who  understands  not  only  the  letter 
but  also  the  reason  of  the  law  will  not  be  at  a  loss 
when  confronted  with  cases  to  which  the  letter  does 
not  accurately  apply.  And  this  is  the  case  with  the 
principle  of  least  superficial  area.  It  is  a  sure  guide 
for  us  even  in  cases  in  which  the  above-stated  para- 
graphs are  not  applicable. 

Our  first  task  will  now  be,  to  show  by  a  palpable 
illustration  the  mode  of  formation  of  liquid  figures  by 
the  principle  of  least  superficial  area.  The  oil  on  the 
wire  pyramid  in  our  mixture  of  alcohol  and  water,  be- 
ing unable  to  leave  the  wire  edges,  clings  to  them,  and 
the  given  mass  of  oil  strives  so  to  shape  itself  that  its 
surface  shall  have  the  least  possible  area.  Suppose 
we  attempt  to  imitate  this  phenomenon.  We  take  a 
wire  pyramid,  draw  over  it  a  stout  film  of  rubber,  and 
in  place  of  the  wire  handle  insert  a  small  tube  leading 


THE  FORMS  OF  LIQUIDS.  n 

into  the  interior  of  the  space  enclosed  by  the  rubber 
(Fig.  3).  Through  this  tube  we  can  blow  in  or  suck 
out  air.  The  quantity  of  air  in  the  enclosure  repre- 
sents the  quantity  of  oil.  The  stretched  rubber  film, 
which,  clinging  to  the  wire  edges, 
does  its  utmost  to  contract,  rep- 
resents the  surface  of  the  oil  en- 
deavoring to  decrease  its  area.  By 
blowing  in,  and  drawing  out  the  air, 
now,  we  actually  obtain  all  the  oil 
pyramidal  figures,  from  those  bulged 
out  to  those  hollowed  in.  Finally,  when 
all  the  air  is  pumped  or  sucked  out,  the 
soap-film  figure  is  exhibited.  The  rub-  Fie-3. 

ber  films  strike  together,  assume  the  form  of  planes, 
and  meet  at  four  sharp  edges  in  the  centre  of  the 
pyramid. 


Fig.  4. 

The  tendency  of  soap-films  to  assume  smaller  forms 
may  be  directly  demonstrated  by  a  method  of  Van  der 
Mensbrugghe.  If  we  dip  a  square  wire  frame  to  which 


I2  THE  FORMS  OF  LIQUIDS. 

a  handle  is  attached  into  a  solution  of  soap  and  water, 
we  shall  obtain  on  the  frame  a  beautiful,  plane  film  of 
soap-suds.  (Fig.  4.)  On  this  we  lay  a  thread  having  its 
two  ends  tied  together.  If,  now,  we  puncture  the  part 
enclosed  by  the  thread,  we  shall  obtain  a  soap-film 
having  a  circular  hole  in  it,  whose  circumference  is 
the  thread.  The  remainder  of  the  film  decreasing  in 
area  as  much  as  it  can,  the  hole  assumes  the  largest 
area  that  it  can.  But  the  figure  of  largest  area,  with 
a  given  periphery,  is  the  circle. 


Fig.  5- 

Similarly,  by  the  principle  of  least  superficial  area, 
a  freely  suspended  mass  of  oil  assumes  the  shape  of  a 
sphere.  The  sphere  is  the  form  of  least  surface  for  a 
given  content.  This  is  evident.  The  more  we  put 
into  a  travelling-bag,  the  nearer  its  shape  approaches 
the  spherical  form. 

The  connexion  of  the  two  above-mentioned  para- 
graphs with  the  principle  of  least  superficial  area  may 
be  shown  by  a  yet  simpler  example.  Picture  to  your- 
selves four  fixed  pulleys,  a,  b,  c,  dt  and  two  movable 


THE  FORMS  OF  LIQUIDS.  13 

rings/,  g  (Fig  5);  about  the  pulleys  and  through  the 
rings  imagine  a  smooth  cord  passed,  fastened  at  one 
extremity  to  a  nail «?,  and  loaded  at  the  other  with  a 
weight  h.  Now  this  weight  always  tends  to  sink,  or, 
what  is  the  same  thing,  always  tends  to  make  the  por- 
tion of  the  string  e  h  as  long  as  possible,  and  conse- 
quently the  remainder  of  the  string,  wound  round  the 
pulleys,  as  short  as  possible.  The  strings  must  remain 
connected  with  the  pulleys,  and  on  account  of  the  rings 
also  with  each  other.  The  conditions  of  the  case,  ac- 
cordingly, are  similar  to  those  of  the  liquid  figures  dis- 
cussed. The  result  also  is  a  similar  one.  When,  as 
in  the  right  hand  figure  of  the  cut,  four  pairs  of  strings 
meet,  a  different  configuration  must  be  established. 
The  consequence  of  the  endeavor  of  the  string  to 
shorten  itself  is  that  the  rings  separate  from  each  other, 
and  that  now  at  all  points  only  three  pairs  of  strings 
meet,  every  two  at  equal  angles  of  one  hundred  and 
twenty  degrees.  As  a  fact,  by  this  arrangement  the 
greatest  possible  shortening  of  the  string  is  attained  j 
as  can  be  easily  proved  by  geometry. 

This  will  help  us  to  some  extent  to  understand  the 
creation  of  beautiful  and  complicated  figures  by  the 
simple  tendency  of  liquids  to  assume  surfaces  of  least 
superficial  area.  But  the  question  arises,  Why  do 
liquids  seek  surfaces  of  least  superficial  area? 

The  particles  of  a  liquid  cling  together.  Drops 
brought  into  contact  coalesce.  We  can  say,  liquid 
particles  attract  each  other.  If  so,  they  seek  to  come 


I4  THE  FORMS  OF  LIQUIDS. 

as  close  as  they  can  to  each  other.  The  particles  at 
the  surface  will  endeavor  to  penetrate  as  far  as  they 
can  into  the  interior.  This  process  will  not  stop,  can- 
not stop,  until  the  surface  has  become  as  small  as  un- 
der the  circumstances  it  possibly  can  become,  until  as 
few  particles  as  possible  remain  at  the  surface,  until 
as  many  particles  as  possible  have  penetrated  into  the 
interior,  until  the  forces  of  attraction  have  no  more 
work  to  perform.* 

The  root  of  the  principle  of  least  surface  is  to  be 
sought,  accordingly,  in  another  and  much  simpler 
principle,  which  may  be  illustrated  by  some  such  an- 
alogy as  this.  We  can  conceive  of  the  natural  forces  of 
attraction  and  repulsion  as  purposes  or  intentions  of 
nature.  As  a  matter  of  fact,  that  interior  pressure 
which  we  feel  before  an  act  and  which  we  call  an  in- 
tention or  purpose,  is  not,  in  a  final  analysis,  so  essen- 
tially different  from  the  pressure  of  a  stone  on  its  sup- 
port, or  the  pressure  of  a  magnet  on  another,  that  it  is 
necessarily  unallowable  to  use  for  both  the  same  term 
— at  least  for  well-defined  purposes,  f  It  is  the  pur- 
pose of  nature,  accordingly,  to  bring  the  iron  nearer 
the  magnet,  the  stone  nearer  the  centre  of  the  earth, 
and  so  forth.  If  such  a  purpose  can  be  realised,  it  is 
carried  out.  But  where  she  cannot  realise  her  pur- 


*  In  almost  all  branches  of  physics  that  are  well  worked  out  such  maximal 
and  minimal  problems  play  an  important  part. 

t  Compare  Mach,  VortrSge  Uber  Psychophysik,  Vienna,  1863,  page  41 ;  Cam- 
pendiMmderPhysikfiirMediciner,  Vienna,  1863,  page  234  ;  and  also  The  Science 
of  Mechanics,  Chicago,  1893,  pp.  84  and  464. 


THE  FORMS  OF  LIQUIDS.  15 

poses,  nature  does  nothing.  In  this  respect  she  acts 
exactly  as  a  good  man  of  business  does. 

It  is  a  constant  purpose  of  nature  to  bring  weights 
lower.  We  can  raise  a  weight  by  causing  another, 
larger  weight  to  sink ;  that  is,  by  satisfying  another, 
more  powerful,  purpose  of  nature.  If  we  fancy  we 
are  making  nature  serve  our  purposes  in  this,  it  will 
be  found,  upon  closer  examination,  that  the  contrary 
is  true,  and  that  nature  has  employed  us  to  attain  her 
purposes. 

Equilibrium,  rest,  exists  only,  but  then  always,  when 
nature  is  brought  to  a  halt  in  her  purposes,  when  the 
forces  of  nature  are  as  fully  satisfied  as,  under  the 
circumstances,  they  can  be.  Thus,  for  example,  heavy 
bodies  are  in  equilibrium,  when  their  so-called  centre 
of  gravity  lies  as  low  as  it  possibly  can,  or  when  as 
much  weight  as  the  circumstances  admit  of  has  sunk 
as  low  as  it  can. 

The  idea  forcibly  suggests  itself  that  perhaps  this 
principle  also  holds  good  in  other  realms.  Equilibrium 
exists  also  in  the  state  when  the  purposes  of  the  par- 
ties are  as  fully  satisfied  as  for  the  time  being  they  can 
be,  or,  as  we  may  say,  jestingly,  in  the  language  of 
physics,  when  the  social  potential  is  a  maximum.* 

You  see,  our  miserly  mercantile  principle  is  replete 
with  consequences,  f  The  result  of  sober  research,  it 

*  Like  reflexions  are  found  in  Quetelet,  Du  systtme  sociale. 

tFor  the  full  development  of  this  idea  see  the  essay  "  On  the  Economical 
Nature  of  Physical  Inquiry,"  p.  186,  and  the  chapter  on  "  The  Economy  of 
Science, "  in  my  Mechanics  (Chicago  :  The  Open  Court  Publishing  Company, 
1893!,  p.  481. 


16  THE  FORMS  OF  LIQUIDS, 

has  become  as  fruitful  for  physics  as  the  dry  questions 
of  Socrates  for  science  generally.  If  the  principle 
seems  to  lack  in  ideality,  the  more  ideal  are  the  fruits 
which  it  bears. 

But  why,  tell  me,  should  science  be  ashamed  of 
such  a  principle?  Is  science*  itself  anything  more 
than — a  business  ?  Is  not  its  task  to  acquire  with  the 
least  possible  work,  in  the  least  possible  time,  with  the 
least  possible  thought,  the  greatest  possible  part  of 
eternal  truth  ? 


*  Science  may  be  regarded  as  a  maximum  or  minimum  problem,  exactly 
as  the  business  of  the  merchant.  In  fact,  the  intellectual  activity  of  natural 
inquiry  is  not  so  greatly  different  from  that  exercised  in  ordinary  life  as  is 
usually  supposed. 


THE  FIBRES  OF  CORTI. 


WHOEVER  has  roamed  through  a  beautiful  coun- 
try knows  that  the  tourist's  delights  increase 
with  his  progress.  How  pretty  that  wooded  dell  must 
look  from  yonder  hill !  Whither  does  that  clear  brook 
flow,  that  hides  itself  in  yonder  sedge?  If  I  only 
knew  how  the  landscape  looked  behind  that  mountain! 
Thus  even  the  child  thinks  in  his  first  rambles.  It  is 
also  true  of  the  natural  philosopher. 

The  first  questions  are  forced  upon  the  attention  of 
the  inquirer  by  practical  considerations ;  the  subse- 
quent ones  are  not.  An  irresistible  attraction  draws 
him  to  these ;  a  nobler  interest  which  far  transcends  the 
mere  needs  of  life.  Let  us  look  at  a  special  case. 

For  a  long  time  the  structure  of  the  organ  of  hear- 
ing has  actively  engaged  the  attention  of  anatomists. 
A  considerable  number  of  brilliant  discoveries  has  been 
brought  to  light  by  their  labors,  and  a  splendid  array 
of  facts  and  truths  established.  But  with  these  facts 
a  host  of  new  enigmas  has  been  presented. 

Whilst  in  the  theory  of  the  organisation  and  func- 


18  THE  FIBRES  OF  CORTI. 

tions  of  the  eye  comparative  clearness  has  been  at- 
tained ;  whilst,  hand  in  hand  with  this,  ophthalmology 
has  reached  a  degree  of  perfection  which  the  preced- 
ing century  could  hardly  have  dreamed  of,  and  by  the 
help  of  the  ophthalmoscope  the  observing  physician 
penetrates  into  the  profoundest  recesses  of  the  eye, 
the  theory  of  the  ear  is  still  much  shrouded  in  mys- 
terious darkness,  full  of  attraction  for  the  investi- 
gator. 

Look  at  this  model  of  the  ear.  Even  at  that  fami- 
liar part  by  whose  extent  we  measure  the  quantity  of 
people's  intelligence,  even  at  the  external  ear,  the 
problems  begin.  You  see  here  a  succession  of  helixes 
or  spiral  windings,  at  times  very  pretty,  whose  signi- 
ficance we  cannot  accurately  state,  yet  for  which  there 
must  certainly  be  some  reason. 

The  shell  or  concha  of  the  ear,  a  in  the  annexed 
diagram,  conducts  the  sound  into  the  curved  auditory 
passage  b,  which  is  terminated  by  a  thin  membrane, 
the  so-called  tympanic  membrane,  e.  This  membrane 
is  set  in  motion  by  the  sound,  and  in  its  turn  sets  in 
motion  a  series  of  little  bones  of  very  peculiar  forma- 
tion, c.  At  the  end  of  all  is  the  labyrinth 
d.  The  labyrinth  consists  of  a  group  of 
cavities  filled  with  a  liquid,  in  which  the 

Fig.  e.  innumerable  fibres  of  the  nerve  of  hear- 

ing are  imbedded.  By  the  vibration  of  the  chain  of 
bones  c,  the  liquid  of  the  labyrinth  is  shaken,  and  the 
auditory  nerve  excited.  Here  the  process  of  hearing 


THE  FIBRES  OF  CORTI.  19 

begins.     So  much  is  certain.     But  the  details  of  the 
process  are  one  and  all  unanswered  questions. 

To  these  old  puzzles,  the  Marchese  Corti,  as  late 
as  1851,  added  a  new  enigma.  And,  strange  to  say, 
it  is  this  last  enigma,  which,  perhaps,  has  first  received 
its  correct  solution.  This  will  be  the  subject  of  our 
remarks  to-day. 

Corti  found  in  the  cochlea,  or  snail-shell  of  the 
labyrinth,  a  large  number  of  microscopic  fibres  placed 
side  by  side  in  geometrically  graduated  order.  Accord- 
ing to  Kolliker  their  number  is  three  thousand.  They 
were  also  the  subject  of  investigation  at  the  hands  of 
Max  Schultze  and  Deiters. 

A  description  of  the  details  of  this  organ  would 
only  weary  you,  besides  not  rendering  the  matter  much 
clearer.  I  prefer,  therefore,  to  state  briefly  what  in 
the  opinion  of  prominent  investigators  like  Helmholtz 
and  Fechner  is  the  peculiar  function  of  Corti's  fibres. 
The  cochlea,  it  seems,  contains  a  large  number  of 
elastic  fibres  of  graduated  lengths  (Fig.  7),  to  which 
the  branches  of  the  auditory  nerve  are 
attached.  These  fibres,  called  the  fibres, 
pillars,  or  rods  of  Corti,  being  of  unequal 
length,  must  also  be  of  unequal  elasticity, 
and,  consequently,  pitched  to  different  Fif?-  7- 
notes.  The  cochlea,  therefore,  is  a  species  of  piano- 
forte. 

What,  now,  may  be  the  office  of  this  structure, 
which  is  found  in  no  other  organ  of  sense?  May  it 


20  THE  FIBRES  OF  CORTI. 

not  be  connected  with  some  special  property  of  the 
ear  ?  It  is  quite  probable ;  for  the  ear  possesses  a  very 
similar  power.  You  know  that  it  is  possible  to  fol- 
low the  individual  voices  of  a  symphony.  Indeed,  the 
feat  is  possible  even  in  a  fugue  of  Bach,  where  it  is  cer- 
tainly no  inconsiderable  achievement.  The  ear  can 
pick  out  the  single  constituent  tonal  parts,  not  only  of  a 
harmony,  but  of  the  wildest  clash  of  music  imaginable. 
The  musical  ear  analyses  every  agglomeration  of  tones. 

The  eye  does  not  possess  this  ability.  Who,  for 
example,  could  tell  from  the  mere  sight  of  white,  with- 
out a  previous  experimental  knowledge  of  the  fact, 
that  white  is  composed  of  a  mixture  of  other  colors  ? 
Could  it  be,  now,  that  these  two  facts,  the  property  of 
the  ear  just  mentioned,  and  the  structure  discovered 
by  Corti,  are  really  connected  ?  It  is  very  probable. 
The  enigma  is  solved  if  we  assume  that  every  note  of 
definite  pitch  has  its  special  string  in  this  pianoforte 
of  Corti,  and,  therefore,  its  special  branch  of  the  audi- 
tory nerve  attached  to  that  string.  But  before  I  can 
make  this  point  perfectly  plain  to  you,  I  must  ask 
you  to  follow  me  a  few  steps  into  the  dry  domain  of 
physics. 

Look  at  this  pendulum.  Forced  from  its  position 
of  equilibrium  by  an  impulse,  it  begins  to  swing  with  a 
definite  time  of  oscillation,  dependent  upon  its  length. 
Longer  pendulums  swing  more  slowly,  shorter  ones 
more  quickly.  We  will  suppose  our  pendulum  to  exe- 
cute one  to-and-fro  movement  in  a  second. 


THE  FIBRES  OF  CORTI.  21 

This  pendulum,  now,  can  be  thrown  into  violent 
vibration  in  two  ways ;  either  by  a  single  heavy  im- 
pulse, or  by  a  number  of  properly  communicated  slight 
impulses.  For  example,  we  impart  to  the  pendulum, 
while  at  rest  in  its  position  of  equilibrium,  a  very  slight 
impulse.  It  will  execute  a  very  small  vibration.  As 
it  passes  a  third  time  its  position  of  equilibrium,  a 
second  having  elapsed,  we  impart  to  it  again  a  slight 
shock,  in  the  same  direction  with  the  first.  Again  after 
the  lapse  of  a  second,  on  its  fifth  passage  through  the 
position  of  equilibrium,  we  strike  it  again  in  the  same 
manner  ;  and  so  continue.  You  see,  by  this  process 
the  shocks  imparted  augment  continually  the  motion 
of  the  pendulum.  After  each  slight  impulse,  the  pen- 
dulum reaches  out  a  little  further  in  its  swing,  and 
finally  acquires  a  considerable  motion.* 

But  this  is  not  the  case  under  all  circumstances. 
It  is  possible  only  when  the  impulses  imparted  syn- 
chronise with  the  swings  of  the  pendulum.  If  we 
should  communicate  the  second  impulse  at  the  end  of 
half  a  second  and  in  the  same  direction  with  the  first 
impulse,  its  effects  would  counteract  the  motion  of  the 
pendulum.  It  is  easily  seen  that  our  little  impulses 
help  the  motion  of  the  pendulum  more  and  more,  ac- 
cording as  their  time'  accords  with  the  time  of  the 
pendulum.  If  we  strike  the  pendulum  in  any  other 
time  than  in  that  of  its  vibration,  in  some  instances,  it 
is  true,  we  shall  augment  its  vibration,  but  in  others 

•This  experiment,  with  its  associated  reflexions,  is  due  to  Galileo. 


22  THE  FIBRES  OF  CORTL 

again,  we  shall  obstruct  it.  Our  impulses  will  be  less 
effective  the  more  the  motion  of  our  own  hand  departs 
from  the  motion  of  the  pendulum. 

What  is  true  of  the  pendulum  holds  true  of  every 
vibrating  body.  A  tuning-fork  when  it  sounds,  also 
vibrates.  It  vibrates  more  rapidly  when  its  sound  is 
higher ;  more  slowly  when  it  is  deeper.  The  standard 
A  of  our  musical  scale  is  produced  by  about  four  hun- 
dred and  fifty  vibrations  in  a  second. 

I  place  by  the  side  of  each  other  on  this  table  two 
tuning-forks,  exactly  alike,  resting  on  resonant  cases. 
I  strike  the  first  one  a  sharp  blow,  so  that  it  emits  a 
loud  note,  and  immediately  grasp  it  again  with  my 
hand  to  quench  its  note.  Nevertheless,  you  still  hear 
the  note  distinctly  sounded,  and  by  feeling  it  you  may 
convince  yourselves  that  the  other  fork  which  was  not 
struck  now  vibrates. 

I  now  attach  a  small  bit  of  wax  to  one  of  the  forks. 
It  is  thrown  thus  out  of  tune ;  its  note  is  made  a  little 
deeper.  I  now  repeat  the  same  experiment  with  the 
two  forks,  now  of  unequal  pitch,  by  striking  one  of 
them  and  again  grasping  it  with  my  hand  ;  but  in  the 
present  case  the  note  ceases  the  very  instant  I  touch 
the  fork. 

What  has  happened  here  in  these  two  experiments? 
Simply  this.  The  vibrating  fork  imparts  to  the  air  and 
to  the  table  four  hundred  and  fifty  shocks  a  second, 
which  are  carried  over  to  the  other  fork.  If  the  othet 
fork  is  pitched  to  the  same  note,  that  is  to  say,  if  it 


THE  FIBRES  OF  CORTL  23 

vibrates  when  struck  in  the  same  time  with  the  first, 
then  the  shocks  first  emitted,  no  matter  how  slight  they 
may  be,  are  sufficient  to  throw  the  second  fork  into  rapid 
sympathetic  vibration.  But  when  the  time  of  vibra- 
tion of  the  two  forks  is  slightly  different,  this  does  not 
take  place.  We  may  strike  as  many  forks  as  we  will,  the 
fork  tuned  to  A  is  perfectly  indifferent  to  their  notes ; 
is  deaf,  in  fact,  to  all  except  its  own  j  and  if  you  strike 
three,  or  four,  or  five,  or  any  number  whatsoever,  of 
forks  all  at  the  same  time,  so  as  to  make  the  shocks 
which  come  from  them  ever  so  great,  the  A  fork  will 
not  join  in  with  their  vibrations  unless  another  fork  A 
is  found  in  the  collection  struck.  It  picks  out,  in  other 
words,  from  all  the  notes  sounded,  that  which  accords 
with  it. 

The  same  is  true  of  all  bodies  which  can  yield 
notes.  Tumblers  resound  when  a  piano  is  played,  on 
the  striking  of  certain  notes,  and  so  do  window  panes. 
Nor  is  the  phenomenon  without  analogy  in  other  pro- 
vinces. Take  a  dog  that  answers  to  the  name  "Nero." 
He  lies  under  your  table.  You  speak  of  Domitian, 
Vespasian,  and  Marcus  Aurelius  Antoninus,  you  call 
upon  all  the  names  of  the  Roman  Emperors  that  oc- 
cur to  you,  but  the  dog  does  not  stir,  although  a  slight 
tremor  of  his  ear  tells  you  of  a  faint  response  of  his 
consciousness.  But  the  moment  you  call  "  Nero  "  he 
jumps  joyfully  towards  you.  The  tuning-fork  is  like 
your  dog.  It  answers  to  the  name  A. 

You  smile,  ladies.     You  shake  your  heads.     The 


24  THE  FIBRES  OF  CORTI. 

simile  does  not  catch  your  fancy.  But  I  have  another, 
which  is  very  near  to  you:  and  for  punishment  you  shall 
hear  it.  You,  too,  are  like  tuning-forks.  Many  are  the 
hearts  that  throb  with  ardor  for  you,  of  which  you  take 
no  notice,  but  are  cold.  Yet  what  does  it  profit  you  ! 
Soon  the  heart  will  come  that  beats  in  just  the  proper 
rhythm,  and  then  your  knell,  too,  has  struck.  Then 
your  heart,  too,  will  beat  in  unison,  whether  you  will 
or  no. 

The  law  of  sympathetic  vibration,  here  propounded 
for  sounding  bodies,  suffers  some  modification  for 
bodies  incompetent  to  yield  notes.  Bodies  of  this 
kind  vibrate  to  almost  every  note.  A  high  silk  hat, 
we  know,  will  not  sound ;  but  if  you  will  hold  your 
hat  in  your  hand  when  attending  your  next  concert  you 
will  not  only  hear  the  pieces  played,  but  also  feel  them 
with  your  fingers.  It  is  exactly  so  with  men.  People 
-  j  who  are  themselves  able  to  give  tone  to  their  surround- 
ings, bother  little  about  the  prattle  of  others.  But  the 
person  without  character  tarries  everywhere  :  in  the 
temperance  hall,  and  at  the  bar  of  the  public-house — 
everywhere  where  a  committee  is  formed.  The  high 
silk  hat  is  among  bells  what  the  weakling  is  among 
men  of  conviction. 

A  sonorous  body,  therefore,  always  sounds  when 
its  special  note,  either  alone  or  in  company  with  others, 
is  struck.  We  may  now  go  a  step  further.  What  will 
be  the  behaviour  of  a  group  of  sonorous  bodies  which 
in  the  pitch  of  their  notes  form  a  scale  ?  Let  us  pic- 


THE  FIBRES  OF  CORTI. 


c d  ef ga b c de  f 
Fig.  8. 


ture  to  ourselves,  for  example  (Fig.  8),  a  series  of  rods 
or  strings  pitched  to  the  notes  c  defg.  ....  On  a 
musical  instrument  the  accord  c  e  g  is  struck.  Every 
one  of  the  rods  of  Fig.  8  will  see  if  its  special  note  is 
contained  in  the  accord,  and  if  it  finds 
it,  it  will  respond.  The  rod  c  will  give 
at  once  the  note  c,  the  rod  e  the  note  e, 
the  rod  g  the  note  g.  All  the  other 
rods  will  remain  at  rest,  will  not  sound. 

We  need  not  look  about  us  long 
for  such  an  instrument.  Every  piano 
is  an  instrument  of  this  kind,  with  which  the  experi- 
ment mentioned  may  be  executed  with  splendid  suc- 
cess. Two  pianos  stand  here  by  the  side  of  each  other, 
both  tuned  alike.  We  will  employ  the  first  for  excit- 
ing the  notes,  while  we  will  allow  the  second  to  re- 
spond ;  after  having  first  pressed  upon  the  loud  pedal, 
so  as  to  render  all  the  strings  capable  of  motion. 

Every  harmony  struck  with  vigor  on  the  first  piano 
is  distinctly  repeated  on  the  second.  To  prove  that 
it  is  the  same  strings  that  are  sounded  in  both  pianos, 
we  repeat  the  experiment  in  a  slightly  changed  form. 
We  let  go  the  loud  pedal  of  the  second  piano  and 
pressing  on  the  keys  c  eg  of  that  instrument  vigorously 
strike  the  harmony  ce g  on  the  first  piano.  The  har- 
mony ceg  is  now  also  sounded  on  the  second  piano. 
But  if  we  press  only  on  one  key  g  of  one  piano,  while 
we  strike  ceg  on  the  other,  only  g  will  be  sounded  on 


26  THE  FIBRES  OF  CORTI. 

the  second.  It  is  thus  always  the  like  strings  of  the 
two  pianos  that  excite  each  other. 

The  piano  can  reproduce  any  sound  that  is  com- 
posed of  its  musical  notes.  It  will  reproduce,  for  ex- 
ample, very  distinctly,  a  vowel  sound  that  is  sung  into 
it.  And  in  truth  physics  has  proved  that  the  vowels 
may  be  regarded  as  composed  of  simple  musical 
notes. 

You  see  that  by  the  exciting  of  definite  tones  in  the 
air  quite  definite  motions  are  set  up  with  mechanical 
necessity  in  the  piano.  The  idea  might  be  made  use 
of  for  the  performance  of  some  pretty  pieces  of  wiz- 
ardry. Imagine  a  box  in  which  is  a  stretched  string 
of  definite  pitch.  This  is  thrown  into  motion  as  often 
as  its  note  is  sung  or  whistled.  Now  it  would  not  be 
a  very  difficult  task  for  a  skilful  mechanic  to  so  con- 
struct the  box  that  the  vibrating  cord  would  close  a 
galvanic  circuit  and  open  the  lock.  And  it  would  not 
be  a  much  more  difficult  task  to  construct  a  box  which 
would  open  at  the  whistling  of  a  certain  melody.  Se- 
same !  and  the  bolts  fall.  Truly,  we  should  have  here 
a  veritable  puzzle-lock.  Still  another  fragment  res- 
cued from  that  old  kingdom  of  fables,  of  which  our  day 
has  realised  so  much,  that  world  of  fairy-stories  to 
which  the  latest  contributions  are  Casselli's  telegraph, 
by  which  one  can  write  at  a  distance  in  one's  own  hand, 
and  Prof.  Elisha  Gray's  telautograph.  What  would 
the  good  old  Herodotus  have  said  to  these  things  who 
even  in  Egypt  shook  his  head  at  much  that  he  saw  ? 


THE  FIBRES  OF  CORTI.  27 

€v  ov  niGra,  just  as  simple- heartedly  as  then, 
when  he  heard  of  the  circumnavigation  of  Africa. 

A  new  puzzle-lock!  But  why  invent  one?  Are 
not  we  human  beings  ourselves  puzzle-locks?  Think 
of  the  stupendous  groups  of  thoughts,  feelings,  and 
emotions  that  can  be  aroused  in  us  by  a  word  !  Are 
there  not  moments  in  all  our  lives  when  a  mere  name 
drives  the  blood  to  our  hearts?  Who  that  has  at- 
tended a  large  mass-meeting  has  not  experienced  what 
tremendous  quantities  of  energy  and  motion  can  be 
evolved  by  the  innocent  words,  "  Liberty,  Equality, 
Fraternity." 

But  let  us  return  to  the  subject  proper  of  our  dis- 
course. Let  us  look  again  at  our  piano,  or  what  will 
do  just  as  well,  at  some  other  contrivance  of  the  same 
character.  What  does  this  instrument  do  ?  Plainly, 
it  decomposes,  it  analyses  every  agglomeration  of 
sounds  set  up  in  the  air  into  its  individual  component 
parts,  each  tone  being  taken  up  by  a  different  string ; 
it  performs  a  real  spectral  analysis  of  sound.  A  person 
completely  deaf,  with  the  help  of  a  piano,  simply  by 
touching  the  strings  or  examining  their  vibrations  with 
a  microscope,  might  investigate  the  sonorous  motion  of 
the  air,  and  pick  out  the  separate  tones  excited  in  it. 

The  ear  has  the  same  capacity  as  this  piano.  The 
ear  performs  for  the  mind  what  the  piano  performs  for 
a  person  who  is  deaf.  The  mind  without  the  ear  is 
deaf.  But  a  deaf  person,  with  the  piano,  does  hear 
after  a  fashion,  though  much  less  vividly,  and  more 


28  THE  FIBRES  OF  CORTI. 

clumsily,  than  with  the  ear.  The  ear,  thus,  also  de- 
composes sound  into  its  component  tonal  parts.  I  shall 
now  not  be  deceived,  I  think,  if  I  assume  that  you 
already  have  a  presentiment  of  what  the  function  of 
Corti's  fibres  is.  We  can  make  the  matter  very  plain  to 
ourselves.  We  will  use  the  one  piano  for  exciting  the 
sounds,  and  we  shall  imagine  the  second  one  in  the 
ear  of  the  observer  in  the  place  of  Corti's  fibres,  which 
is  a  model  of  such  an  instrument.  To  every  string  of 
the  piano  in  the  ear  we  will  suppose  a  special  fibre  of 
the  auditory  nerve  attached,  so  that  this  fibre  and  this 
alone,  is  irritated  when  the  string  is  thrown  into  vibra- 
tion. If  we  strike  now  an  accord  on  the  external 
piano,  for  every  tone  of  that  accord  a  definite  string  of 
the  internal  piano  will  sound  and  as  many  different 
nervous  fibres  will  be  irritated  as  there  are  notes  in 
the  accord.  The  simultaneous  sense-impressions  due 
to  different  notes  can  thus  be  preserved  unmingled  and 
be  separated  by  the  attention.  It  is  the  same  as  with 
the  five  fingers  of  the  hand.  With  each  finger  I  can 
touch  something  different.  Now  the  ear  has  three  thou- 
sand such  fingers,  and  each  one  is  designed  for  the 
touching  of  a  different  tone.*  Our  ear  is  a  puzzle-lock 
of  the  kind  mentioned.  It  opens  at  the  magic  melody 
of  a  sound.  But  it  is  a  stupendously  ingenious  lock. 
Not  only  one  tone,  but  every  tone  makes  it  open  ;  but 

•A  development  of  the  theory  of  musical  audition  differing  in  many 
points  from  the  theory  of  Helmholtz  here  expounded,  will  be  found  in  my 
Contributions  to  the  Analysis  of  the  Sensations  (English  translation  by  C.  M. 
Williams),  Chicago,  The  Open  Court  Publishing  Company,  1897. 


THE  FIBRES  OF  CORTI.  29 

each  one  differently.  To  each  tone  it  replies  with  a 
different  sensation. 

More  than  once  it  has  happened  in  the  history  of 
science  that  a  phenomenon  predicted  by  theory,  has 
not  been  brought  within  the  range  of  actual  observa- 
tion until  long  afterwards.  Leverrier  predicted  the 
existence  and  the  place  of  the  planet  Neptune,  but  it 
was  not  until  sometime  later  that  Galle  actually  found 
the  planet  at  the  predicted  spot.  Hamilton  unfolded 
theoretically  the  phenomenon  of  the  so-called  conical 
refraction  of  light,  but  it  was  reserved  for  Lloyd  some 
time  subsequently  to  observe  the  fact.  The  fortunes 
of  Helmholtz's  theory  of  Corti's  fibres  have  been  some- 
what similar.  This  theory,  too,  received  its  substan- 
tial confirmation  from  the  subsequent  observations  of 
V.  Hensen.  On  the  free  surface  of  the  bodies  of  Crusta- 
cea, connected  with  the  auditory  nerves,  rows  of  lit- 
tle hairy  filaments  of  varying  lengths  and  thicknesses 
are  found,  which  to  some  extent  are  the  analogues  of 
Corti's  fibres.  Hensen  saw  these  hairs  vibrate  when 
sounds  were  excited,  and  when  different  notes  were 
struck  different  hairs  were  set  in  vibration. 

I  have  compared  the  work  of  the  physical  inquirer 
to  the  journey  of  the  tourist.  When  the  tourist  as- 
cends a  new  hill  he  obtains  of  the  whole  district  a 
different  view.  When  the  inquirer  has  found  the  so- 
lution of  one  enigma,  the  solution  of  a  host  of  others 
falls  into  his  hands. 

Surely  you  have  often  felt  the  strange  impression  ex- 


36  THE  FIBRES  OF  CORTI. 

perienced  when  in  singing  through  the  scale  the  octave 
is  reached,  and  nearly  the  same  sensation  is  produced 
as  by  the  fundamental  tone.  The  phenomenon  finds  its 
explanation  in  the  view  here  laid  down  of  the  ear.  And 
not  only  this  phenomenon  but  all  the  laws  of  the  the- 
ory of  harmony  may  be  grasped  and  verified  from  this 
point  of  view  with  a  clearness  before  undreamt  of. 
Unfortunately,  I  must  content  myself  to-day  with  the 
simple  indication  of  these  beautiful  prospects.  Their 
consideration  would  lead  us  too  far  aside  into  the  fields 
of  other  sciences. 

The  searcher  of  nature,  too,  must  restrain  himself 
in  his  path.  He  also  is  drawn  along  from  one  beauty 
to  another  as  the  tourist  from  dale  to  dale,  and  as  cir- 
cumstances generally  draw  men  from  one  condition  of 
life  into  others.  It  is  not  he  so  much  that  makes  the 
quests,  as  that  the  quests  are  made  of  him.  Yet  let 
him  profit  by  his  time,  and  let  not  his  glance  rove  aim- 
lessly hither  and  thither.  For  soon  the  evening  sun 
will  shine,  and  ere  he  has  caught  a  full  glimpse  of  the 
wonders  close  by,  a  mighty  hand  will  seize  him  and 
lead  him  away  into  a  different  world  of  puzzles. 

Respected  hearers,  science  once  stood  in  an  en- 
tirely different  relation  to  poetry.  The  old  Hindu 
mathematicians  wrote  their  theorems  in  verses,  and 
lotus-flowers,  roses,  and  lilies,  beautiful  sceneries, 
lakes,  and  mountains  figured  in  their  problems. 

"Thou  goest  forth  on  this  lake  in  a  boat.  A  lily 
juts  forth,  one  palm  above  the  water.  A  breeze  bends 


THE  FIBRES  OF  CORTI.  31 

it  downwards,  and  it  vanishes  two  palms  from  its  pre- 
vious spot  beneath  the  surface.  Quick,  mathemati- 
cian, tell  me  how  deep  is  the  lake  !  " 

Thus  spoke  an  ancient  Hindu  scholar.  This  poetry, 
and  rightly,  has  disappeared  from  science,  but  from 
its  dry  leaves  another  poetry  is  wafted  aloft  which  can- 
not be  described  to  him  who  has  never  felt  it.  Who- 
ever will  fully  enjoy  this  poetry  must  put  his  hand  to 
the  plough,  must  himself  investigate.  Therefore, 
enough  of  this  !  I  shall  reckon  myself  fortunate  if  you 
do  not  repent  of  this  brief  excursion  into  the  flowered 
dale  of  physiology,  and  if  you  take  with  yourselves  the 
belief  that  we  can  say  of  science  what  we  say  of  poetry, 

"  Who  the  song  would  understand, 
Needs  must  seek  the  song's  own  land; 
Who  the  minstrel  understand 
Needs  must  seek  the  minstrel's  land." 


ON  THE  CAUSES  OF  HARMONY. 


WE  are  to  speak  to-day  of  a  theme  which  is  perhaps 
of  somewhat  more  general  interest — the  causes  of 
the  harmony  of  musical  sounds.  The  first  and  simplest 
experiences  relative  to  harmony  are  very  ancient.  Not 
so  the  explanation  of  its  laws.  These  were  first  sup- 
plied by  the  investigators  of  a  recent  epoch.  Allow  me 
an  historical  retrospect. 

Pythagoras  (586  B.  C.)  knew  that  the  note  yielded 
by  a  string  of  steady  tension  was  converted  into  its 
octave  when  the  length  of  the  string  was  reduced  one- 
half,  and  into  its  fifth  when  reduced  two-thirds ;  and 
that  then  the  first  fundamental  tone  was  consonant 
with  the  two  others.  He  knew  generally  that  the  same 
string  under  fixed  tension  gives  consonant  tones  when 
successively  divided  into  lengths  that  are  in  the  pro- 
portions of  the  simplest  natural  numbers ;  that  is,  in 
the  proportions  of  1:2,  2:3,  3:4,  4:5. 

Pythagoras  failed  to  reveal  the  causes  of  these  laws. 
What  have  consonant  tones  to  do  with  the  simple  nat- 
ural numbers  ?  That  is  the  question  we  should  ask 


ON  THE  CAUSES  OF  HARMONY.  33 

to-day.  But  this  circumstance  must  have  appeared 
less  strange  than  inexplicable  to  Pythagoras.  This 
philosopher  sought  for  the  causes  of  harmony  in  the 
occult,  miraculous  powers  of  numbers.  His  procedure 
was  largely  the  cause  of  the  upgrowth  of  a  numerical 
mysticism,  of  which  the  traces  may  still  be  detected  in 
our  oneirocritical  books  and  among  some  scientists,  to 
whom  marvels  are  more  attractive  than  lucidity. 

Euclid  (300  B.  C.)  gives  a  definition  of  consonance 
and  dissonance  that  could  hardly  be  improved  upon, 
in  point  of  verbal  accuracy.  The  consonance  (GV^JL- 
cpoovia)  of  two  tones,  he  says,  is  the  mixture,  the 
blending  (xpaffiS')  of  those  two  tones ;  dissonance 
(Siatpwvia'},  on  the  other  hand,  is  the  incapacity  of 
the  tones  to  blend  (a//z£/or),  whereby  they  are  made 
harsh  for  the  ear.  The  person  who  knows  the  correct 
explanation  of  the  phenomenon  hears  it,  so  to  speak, 
reverberated  in  these  words  of  Euclid.  Still,  Euclid 
did  not  know  the  true  cause  of  harmony.  He  had  un- 
wittingly come  very  near  to  the  truth,  but  without 
really  grasping  it. 

Leibnitz  (1646-1716  A.  D.)  resumed  the  question 
which  his  predecessors  had  left  unsolved.  He,  of 
course,  knew  that  musical  notes  were  produced  by  vi- 
brations, that  twice  as  many  vibrations  corresponded 
to  the  octave  as  to  the  fundamental  tone,  etc.  A  pas- 
sionate lover  of  mathematics,  he  sought  for  the  cause 
of  harmony  in  the  secret  computation  and  comparison 
of  the  simple  numbers  of  vibrations  and  in  the  secret 


34  ON  THE  CAUSES  OF  HARMONY. 

satisfaction  of  the  soul  at  this  occupation.  But  how, 
we  ask,  if  one  does  not  know  that  musical  notes  are 
vibrations  ?  The  computation  and  the  satisfaction  at 
the  computation  must  indeed  be  pretty  secret  if  it  is 
unknown.  What  queer  ideas  philosophers  have!  Could 
anything  more  wearisome  be  imagined  than  computa- 
tion as  a  principle  of  aesthetics  ?  Yes,  you  are  not 
utterly  wrong  in  your  conjecture,  yet  you  may  be  sure 
that  Leibnitz's  theory  is  not  wholly  nonsense,  although 
it  is  difficult  to  make  out  precisely  what  he  meant  by 
his  secret  computation. 

The  great  Euler  (1707-1783)  sought  the  cause  of 
harmony,  almost  as  Leibnitz  did,  in  the  pleasure  which 
the  soul  derives  from  the  contemplation  of  order  in  the 
numbers  of  the  vibrations.* 

Rameau  and  D'Alembert  (1717-1783)  approached 
nearer  to  the  truth.  They  knew  that  in  every  sound 
available  in  music  besides  the  fundamental  note  also 
the  twelfth  and  the  next  higher  third  could  be  heard ; 
and  further  that  the  resemblance  between  a  fundamen- 
tal tone  and  its  octave  was  always  strongly  marked. 
Accordingly,  the  combination  of  the  octave,  fifth,  third, 
etc.,  with  the  fundamental  tone  appeared  to  them  "nat- 
ural." They  possessed,  we  must  admit,  the  correct 
point  of  view ;  but  with  the  simple  naturalness  of  a 
phenomenon  no  inquirer  can  rest  content ;  for  it  is  pre- 

*  Sauveur  also  set  out  from  Leibnitz's  idea,  but  arrived  by  independent 
researches  at  a  different  theory,  which  was  very  near  to  that  of  Helmholtz. 
Compare  on  this  point  Sauveur,  Mimoires  de  P Academic  ties  Sciences,  Paris, 
1700-1705,  and  R.  Smith,  Harmonics,  Cambridge,  1749.  (See  Appendix,  p.  346.) 


ON  THE  CAUSES  OF  HARMONY.  35 

cisely  this  naturalness  for  which  he  seeks  his  explana- 
tions. 

Rameau's  remark  dragged  along  through  the  whole 
modern  period,  but  without  leading  to  the  full  discov- 
ery of  the  truth.  Marx  places  it  at  the  head  of  his 
theory  of  composition,  but  makes  no  further  applica- 
tion of  it.  Also  Goethe  and  Zelter  in  their  correspon- 
dence were,  so  to  speak,  on  the  brink  of  the  truth. 
Zelter  knew  of  Rameau's  view.  Finally,  you  will  be 
appalled  at  the  difficulty  of  the  problem,  when  I  tell 
you  that  till  very  recent  times  even  professors  of  phys- 
ics were  dumb  when  asked  what  were  the  causes  of 
harmony. 

Not  till  quite  recently  did  Helmholtz  find  the  so- 
lution of  the  question.  But  to  make  this  solution  clear 
to  you  I  must  first  speak  of  some  experimental  prin- 
ciples of  physics  and  psychology. 

i)  In  every  process  of  perception,  in  every  obser- 
vation, the  attention  plays  a  highly  important  part. 
We  need  not  look  about  us  long  for  proofs  of  this. 
You  receive,  for  example,  a  letter  written  in  a  very 
poor  hand.  Do  your  best,  you  cannot  make  it  out. 
You  put  together  now  these,  now  those  lines,  yet  you 
cannot  construct  from  them  a  single  intelligible  char- 
acter. Not  until  you  direct  your  attention  to  groups 
of  lines  which  really  belong  together,  is  the  reading  of 
the  letter  possible.  Manuscripts,  the  letters  of  which 
are  formed  of  minute  figures  and  scrolls,  can  only  be 
read  at  a  considerable  distance,  where  the  attention  is 


36  ON  THE  CA  USES  OF  HARMONY. 

no  longer  diverted  from  the  significant  outlines  to  the 
details.  A  beautiful  example  of  this  class  is  furnished 
by  the  famous  iconographs  of  Giuseppe  Arcimboldo  in 
the  basement  of  the  Belvedere  gallery  atVienna.  These 
are  symbolic  representations  of  water,  fire,  etc.  :  hu- 
man heads  composed  of  aquatic  animals  and  of  com- 
bustibles. At  a  short  distance  one  sees  only  the  de- 
tails, at  a  greater  distance  only  the  whole  figure.  Yet 
a  point  can  be  easily  found  at  which,  by  a  simple  vol- 
untary movement  of  the  attention,  there  is  no  difficulty 
in  seeing  now  the  whole  figure  and  now  the  smaller 
forms  of  which  it  is  composed.  A  picture  is  often  seen 
representing  the  tomb  of  Napoleon.  The  tomb  is  sur- 
rounded by  dark  trees  between  which  the  bright  heav- 
ens are  visible  as  background.  One  can  look  a  long  time 
at  this  picture  without  noticing  anything  except  the 
trees,  but  suddenly,  on  the  attention  being  acciden- 
tally directed  to  the  bright  background,  one  sees 
the  figure  of  Napoleon  between  the  trees.  This  case 
shows  us  very  distinctly  the  important  part  which  at- 
tention plays.  The  same  sensuousi  object  can,  solely 
by  the  interposition  of  attention,  give  rise  to  wholly 
different  perceptions. 

If  I  strike  a  harmony,  or  chord,  on  this  piano,  by 
a  mere  effort  of  attention  you  can  fix  every  tone  of 
that  harmony.  You  then  hear  most  distinctly  the 
fixed  tone,  and  all  the  rest  appear  as  a  mere  addition, 
altering  only  the  quality,  or  acoustic  color,  of  the  pri- 
mary tone.  The  effect  of  the  same  harmony  is  essen- 


ON  THE  CAUSES  OF  HARMONY.  37 

tially  modified  if  we  direct  our  attention  to  different 
tones. 

Strike  in  succession  two  harmonies,  for  example, 
the  two  represented  in  the  annexed  diagram,  and  first 
fix  by  the  attention  the  upper  note  e,  afterwards  the 
base  e — a ;  in  the  two  cases  you  will  hear  the  same 
sequence  of  harmonies  differently. 
In  the  first  case,  you  have  the  im- 
pression as  if   the  fixed  tone  re- 
mained unchanged  and  simply  al- 
tered its  timbre ;  in  the  second  case, 
the  whole  acoustic   agglomeration 
seems  to   fall    sensibly   in   depth. 
There  is  an  art  of  composition  to  guide  the  attention 
of  the  hearer.     But  there  is  also  an  art  of  hearing, 
which  is  not  the  gift  of  every  person. 

The  piano-player  knows  the  remarkable  effects  ob- 
tained when  one  of  the  keys  of  a  chord  that  is  struck 


ivy    g   i  \o   i'  ^g= 


7^~H    g^     ^ 

f^T^T 


is  let  loose.  Bar  i  played  on  the  piano  sounds  almost 
like  bar  2.  The  note  which  lies  next  to  the  key  let 
loose  resounds  after  its  release  as  if  it  were  freshly 
struck.  The  attention  no  longer  occupied  with  the 
upper  note  is  by  that  very  fact  insensibly  led  to  the 
upper  note. 


38  ON  THE  CAUSES  OF  HARMONY. 

Any  tolerably  cultivated  musical  ear  can  perform 
the  resolution  of  a  harmony  into  its  component  parts. 
By  much  practice  we  can  go  even  further.  Then, 
every  musical  sound  heretofore  regarded  as  simple 
can  be  resolved  into  a  subordinate  suc- 
cession of  musical  tones.  For  example, 
if  I  strike  on  the  piano  the  note  i,  (an- 
nexed diagram,)  we  shall  hear,  if  we 
make  the  requisite  effort  of  attention, 
besides  the  loud  fundamental  note  the 
feebler,  higher  overtones,  or  harmonics, 
2 ....  7,  that  is,  the  octave,  the  twelfth,  the  double 
octave,  and  the  third,  the  fifth,  and  the  seventh  of 
the  double  octave. 

The  same  is  true  of  every  musically  available 
sound.  Each  yields,  with  varying  degrees  of  inten- 
sity, besides  its  fundamental  note,  also  the  octave,  the 
twelfth,  the  double  octave,  etc.  The  phenomenon  is 
observable  with  special  facility  on  the  open  and  closed 
flue-pipes  of  organs.  According,  now,  as  certain  over- 
tones are  more  or  less  distinctly  emphasised  in  a 
sound,  the  timbre  of  the  sound  changes — that  peculiar 
quality  of  the  sound  by  which  we  distinguish  the  music 
of  the  piano  from  that  of  the  violin,  the  clarinet,  etc. 
On  the  piano  these  overtones  can  be  very  easily 
rendered  audible.  If  I  strike,  for  example,  sharply 
note  i  of  the  foregoing  series,  whilst  I  simply  press 
down  upon,  one  after  another,  the  keys  2,  3,  ....  7, 
the  notes  2,  3,  ....  7  will  continue  to  sound  after  the 


ON  THE  CAUSES  OF  HARMONY.  39 

striking  of  i,  because  the  strings  corresponding  to 
these  notes,  now  freed  from  their  dampers,  are  thrown 
into  sympathetic  vibration. 

As  you  know,  this  sympathetic  vibration  of  the  like- 
pitched  strings  with  the  overtones  is  really  not  to  be 
conceived  as  sympathy,  but  rather  as  lifeless  mechani- 
cal necessity.  We  must  not  think  of  this  sympathetic 
vibration  as  an  ingenious  journalist  pictured  it,  who 
tells  a  gruesome  story  of  Beethoven's  F  minor  sonata, 
Op.  2,  that  I  cannot  withhold  from  you.  "At  the 
last  London  Industrial  Exhibition  nineteen  virtuosos 
played  the  F  minor  sonata  on  the  same  piano.  When 
the  twentieth  stepped  up  to  the  instrument  to  play  by 
way  of  variation  the  same  production,  to  the  terror  of 
all  present  the  piano  began  to  render  the  sonata  of  its 
own  accord.  The  Archbishop  of  Canterbury,  who 
happened  to  be  present,  was  set  to  work  and  forthwith 
expelled  the  F  minor  devil." 

Although,  now,  the  overtones  or  harmonics  which 
we  have  discussed  are  heard  only  upon  a  special  effort 
of  the  attention,  nevertheless  they  play  a  highly  im- 
portant part  in  the  formation  of  musical  timbre,  as  also 
in  the  production  of  the  consonance  and  dissonance  of 
sounds.  This  may  strike  you  as  singular.  How  can 
a  thing  which  is  heard  only  under  exceptional  circum- 
stances be  of  importance  generally  for  audition  ? 

But  consider  some  familiar  incidents  of  your  every- 
day life.  Think  of  how  many  things  you  see  which 
you  do  not  notice,  which  never  strike  your  attention 


40  ON  THE  CAUSES  OF  HARMONY. 

until  they  are  missing.  A  friend  calls  upon  you  ;  you 
cannot  understand  why  he  looks  so  changed.  Not 
until  you  make  a  close  examination  do  you  discover 
that  his  hair  has  been  cut.  It  is  not  difficult  to  tell 
the  publisher  of  a  work  from  its  letter-press,  and  yet 
no  one  can  state  precisely  the  points  by  which  this 
style  of  type  is  so  strikingly  different  from  that  style. 
I  have  often  recognised  a  book  which  I  was  in  search 
of  from  a  simple  piece  of  unprinted  white  paper  that 
peeped  out  from  underneath  the  heap  of  books  cover- 
ing it,  and  yet  I  had  never  carefully  examined  the 
paper,  nor  could  I  have  stated  its  difference  from  other 
papers. 

What  we  must  remember,  therefore,  is  that  every 
sound  that  is  musically  available  yields,  besides  its 
fundamental  note,  its  octave,  its  twelfth,  its  double 
octave,  etc.,  as  overtones  or  harmonics,  and  that  these 
are  important  for  the  agreeable  combination  of  several 
musical  sounds. 

2)  One  other  fact  still  remains  to  be  dealt  with. 
Look  at  this  tuning-fork.  It  yields,  when  struck,  a  per- 
fectly smooth  tone.  But  if  you  strike  in  company  with 
it  a  second  fork  which  is  of  slightly  different  pitch,  and 
which  alone  also  gives  a  perfectly  smooth  tone,  you 
will  hear,  if  you  set  both  forks  on  the  table,  or  hold 
both  before  your  ear,  a  uniform  tone  no  longer,  but  a 
number  of  shocks  of  tones.  The  rapidity  of  the  shocks 
increases  with  the  difference  of  the  pitch  of  the  forks. 
These  shocks,  which  become  very  disagreeable  for  the 


ON  THE  CAUSES  OF  HARMONY.  41 

ear  when  they  amount  to  thirty-three  in  a  second,  are 
called  "beats." 

Always,  when  one  of  two  like  musical  sounds  is 
thrown  out  of  unison  with  the  other,  beats  arise.  Their 
number  increases  with  the  divergence  from  unison,  and 
simultaneously  they  grow  more  unpleasant.  Their 
roughness  reaches  its  maximum  at  about  thirty-three 
beats  in  a  second.  On  a  still  further  departure  from 
unison,  and  a  consequent  increase  of  the  number  of 
beats,  the  unpleasant  effect  is  diminished,  so  that  tones 
which  are  widely  apart  in  pitch  no  longer  produce 
offensive  beats. 

To  give  yourselves  a  clear  idea  of  the  production 
of  beats,  take  two  metronomes  and  set  them  almost 
alike.  You  can,  for  that  matter,  set  the  two  exactly 
alike.  You  need  not  fear  that  they  will  strike  alike. 
The  metronomes  usually  for  sale  in  the  shops  are  poor 
enough  to  yield,  when  set  alike,  appreciably  unequal 
strokes.  Set,  now,  these  two  metronomes,  which  strike 
at  unequal  intervals,  in  motion  ;  you  will  readily  see 
that  their  strokes  alternately  coincide  and  conflict  with 
each  other.  The  alternation  is  quicker  the  greater  the 
difference  of  time  of  the  two  metronomes. 

If  metronomes  are  not  to  be  had,  the  experiment 
may  be  performed  with  two  watches. 

Beats  arise  in  the  same  way.  The  rhythmical 
shocks  of  two  sounding  bodies,  of  unequal  pitch,  some- 
times coincide,  sometimes  interfere,  whereby  they  al- 


ON  THE  CAUSES  OF  HARMONY, 


ternately  augment  and  enfeeble  each  other's  effects. 
Hence  the  shock-like,  unpleasant  swelling  of  the  tone. 
Now  that  we  have  made  ourselves  acquainted  with 
overtones  and  beats,  we  may  proceed  to  the  answer  of 
our  main  question,  Why  do  certain  relations  of  pitch 
produce  pleasant  sounds,  consonances,  others  unpleas- 
ant sounds,  dissonances  ?  It  will  be  readily  seen  that 
all  the  unpleasant  effects  of  simultaneous  sound-com- 
binations are  the  result  of  beats  produced  by  those 
combinations.  Beats  are  the  only  sin,  the  sole  evil  of 
music.  Consonance  is  the  coalescence  of  sounds  with- 
out appreciable  beats. 


Fig.  12. 

To  make  this  perfectly  clear  to  you  I  have  con- 
structed the  model  which  you  see  in  Fig.  12.  It  rep- 
resents a  claviatur.  At  its  top  a  movable  strip  of  wood 
aa  with  the  marks  i,  2  ....  6  is  placed.  By  setting 
this  strip  in  any  position,  for  example,  in  that  where  the 
mark  i  is  over  the  note  c  of  the  claviatur,  the  marks 
2,  3  ....  6,  as  you  see,  stand  over  the  overtones  of  c. 
The  same  happens  when  the  strip  is  placed  in  any 
other  position.  A  second,  exactly  similiar  strip,  bb, 
possesses  the  same  properties.  Thus,  together,  the 
two  strips,  in  any  two  positions,  point  out  by  their 


ON  THE  CA  USES  OF  HARMONY.  43 

marks  all  the  tones  brought  into  play  upon  the  simulta- 
neous sounding  of  the  notes  indicated  by  the  marks  i. 

The  two  strips,  placed  over  the  same  fundamental 
note,  show  that  also  all  the  overtones  of  those  notes 
coincide.  The  first  note  is  simply  intensified  by  the 
other.  The  single  overtones  of  a  sound  lie  too  far  apart 
to  permit  appreciable  beats.  The  second  sound  sup- 
plies nothing  new,  consequently,  also,  no  new  beats. 
Unison  is  the  most  perfect  consonance. 

Moving  one  of  the  two  strips  along  the  other  is 
equivalent  to  a  departure  from  unison.  All  the  over- 
tones of  the  one  sound  now  fall  alongside  those  of  the 
other ;  beats  are  at  once  produced ;  the  combination 
of  the  tones  becomes  unpleasant :  we  obtain  a  disso- 
nance. If  we  move  the  strip  further  and  further  along, 
we  shall  find  that  as  a  general  rule  the  overtones  al- 
ways fall  alongside  each  other,  that  is,  always  produce 
beats  and  dissonances.  Only  in  a  few  quite  definite 
positions  do  the  overtones  partially  coincide.  Such 
positions,  therefore,  signify  higher  degrees  of  euphony 
— they  point  out  the  consonant  intervals. 

These  consonant  intervals  can  be  readily  found  ex- 
perimentally by  cutting  Fig.  12  out  of  paper  and  moving 
bb  lengthwise  along  aa.  The  most  perfect  consonances 
are  the  octave  and  the  twelfth,  since  in  these  two  cases 
the  overtones  of  the  one  sound  coincide  absolutely 
with  those  of  the  other.  In  the  octave,  for  example, 
i  /'falls  on  2  a,  o.b  on  4  a,  $b  on  6  a.  Consonances, 
therefore,  are  simultaneous  sound-combinations  not 


44  ON  THE  CAUSES  OF  HARMONY. 

accompanied  by  disagreeable  beats.  This,  by  the  way, 
is,  expressed  in  English,  what  Euclid  said  in  Greek. 

Only  such  sounds  are  consonant  as  possess  in  com- 
mon some  portion  of  their  partial  tones.  Plainly  we 
must  recognise  between  such  sounds,  also  when  struck 
one  after  another,  a  certain  affinity.  For  the  second 
sound,  by  virtue  of  the  common  overtones,  will  produce 
partly  the  same  sensation  as  the  first.  The  octave  is 
the  most  striking  exemplification  of  this.  When  we 
reach  the  octave  in  the  ascent  of  the  scale  we  actually 
fancy  we  hear  the  fundamental  tone  repeated.  The 
foundations  of  harmony,  therefore,  are  the  foundations 
of  melody. 

Consonance  is  the  coalescence  of  sounds  without 
appreciable  beats  !  This  principle  is  competent  to  in- 
troduce wonderful  order  and  logic  into  the  doctrines 
of  the  fundamental  bass.  The  compendiums  of  the 
theory  of  harmony  which  (Heaven  be  witness  !)  have 
stood  hitherto  little  behind  the  cook-books  in  subtlety 
of  logic,  are  rendered  extraordinarily  clear  and  simple. 
And  what  is  more,  all  that  the  great  masters,  such  as 
Palestrina,  Mozart,  Beethoven,  unconsciously  got 
right,  and  of  which  heretofore  no  text-book  could  ren- 
der just  account,  receives  from  the  preceding  principle 
its  perfect  verification. 

But  the  beauty  of  the  theory  is,  that  it  bears  upon 
its  face  the  stamp  of  truth.  It  is  no  phantom  of  the 
brain.  Every  musician  can  hear  for  himself  the  beats 
which  the  overtones  of  his  musical  sounds  produce. 


ON  THE  CAUSES  OF  HARMONY.  45 

Every  musician  can  satisfy  himself  that  for  any  given 
case  the  number  and  the  harshness  of  the  beats  can 
be  calculated  beforehand,  and  that  they  occur  in  ex- 
actly the  measure  that  theory  determines. 

This  is  the  answer  which  Helmholtz  gave  to  the 
question  of  Pythagoras,  so  far  as  it  can  be  explained 
with  the  means  now  at  my  command.  A  long  period 
of  time  lies  between  the  raising  and  the  solving  of  this 
question.  More  than  once  were  eminent  inquirers 
nearer  to  the  answer  than  they  dreamed  of. 

The  inquirer  seeks  the  truth.  I  do  not  know  if  the 
truth  seeks  the  inquirer.  But  were  that  so,  then  the 
history  of  science  would  vividly  remind  us  of  that 
classical  rendezvous,  so  often  immortalised  by  paint- 
ers and  poets.  A  high  garden  wall.  At  the  right  a 
youth,  at  the  left  a  maiden.  The  youth  sighs,  the 
maiden  sighs  !  Both  wait.  Neither  dreams  how  near 
the  other  is. 

I  like  this  simile.  Truth  suffers  herself  to  be 
courted,  but  she  has  evidently  no  desire  to  be  won. 
She  flirts  at  times  disgracefully.  Above  all,  she  is  de- 
termined to  be  merited,  and  has  naught  but  contempt 
for  the  man  who  will  win  her  too  quickly.  And  if, 
forsooth,  one  breaks  his  head  in  his  efforts  of  conquest, 
what  matter  is  it,  another  will  come,  and  truth  is  al- 
ways young.  At  times,  indeed,  it  really  seems  as  if 
she  were  well  disposed  towards  her  admirer,  but  that 
admitted — never !  Only  when  Truth  is  in  exceptionally 
good  spirits  does  she  bestow  upon  her  wooer  a  glance 


46  ON  THE  CA  USES  OF  HARMONY. 

of  encouragement.  For,  thinks  Truth,  if  I  do  not  do 
something,  in  the  end  the  fellow  will  not  seek  me  at  all. 

This  one  fragment  of  truth,  then,  we  have,  and  it 
shall  never  escape  us.  But  when  I  reflect  what  it  has 
cost  in  labor  and  in  the  lives  of  thinking  men,  how  it 
painfully  groped  its  way  through  centuries,  a  half- 
matured  thought,  before  it  became  complete ;  when  1 
reflect  that  it  is  the  toil  of  more  than  two  thousand 
years  that  speaks  out  of  this  unobtrusive  model  of 
mine,  then,  without  dissimulation,  I  almost  repent  me 
of  the  jest  I  have  made. 

And  think  of  how  much  we  still  lack !  When,  sev- 
eral thousand  years  hence,  boots,  top-hats,  hoops,  pia- 
nos, and  bass-viols  are  dug  out  of  the  earth,  out  of  the 
newest  alluvium  as  fossils  of  the  nineteenth  century; 
when  the  scientists  of  that  time  shall  pursue  their 
studies  both  upon  these  wonderful  structures  and  upon 
our  modern  Broadways,  as  we  to-day  make  studies  of 
the  implements  of  the  stone  age  and  of  the  prehistoric 
lake-dwellings — then,  too,  perhaps,  people  will  be  un- 
able to  comprehend  how  we  could  come  so  near  to 
many  great  truths  without  grasping  them.  And  thus 
it  is  for  all  time  the  unsolved  dissonance,  for  all  time 
the  troublesome  seventh,  that  everywhere  resounds  in 
our  ears;  we  feel,  perhaps,  that  it  will  find  its  solu- 
tion, but  we  shall  never  live  to  see  the  day  of  the  pure 
triple  accord,  nor  shall  our  remotest  descendants. 

Ladies,  if  it  is  the  sweet  purpose  of  your  life  to 
sow  confusion,  it  is  the  purpose  of  mine  to  be  clear ; 


ON  THE  CAUSES  OF  HARMONY.  47 

and  so  I  must  confess  to  you  a  slight  transgression 
that  I  have  been  guilty  of.  On  one  point  I  have  told 
you  an  untruth.  But  you  will  pardon  me  this  false- 
hood, if  in  full  repentance  I  make  it  good.  The  model 
represented  in  Fig.  12  does  not  tell  the  whole  truth,  for 
it  is  based  upon  the  so-called  "even  temperament" 
system  of  tuning.  The  overtones,  however,  of  musical 
sounds  are  not  tempered,  but  purely  tuned.  By  means 
of  this  slight  inexactness  the  model  is  made  consider- 
ably simpler.  In  this  form  it  is  fully  adequate  for 
ordinary  purposes,  and  no  one  who  makes  use  of  it  in 
his  studies  need  be  in  fear  of  appreciable  error. 

If  you  should  demand  of  me,  however,  the  full 
truth,  I  could  give  you  that  only  by  the  help  of  a  math- 
ematical formula.  I  should  have  to  take  the  chalk  into 
my  hands  and — think  of  it ! — reckon  in  your  presence. 
This  you  might  take  amiss.  Nor  shall  it  happen. 
I  have  resolved  to  do  no  more  reckoning  for  to-day. 
I  shall  reckon  now  only  upon  your  forbearance,  and 
this  you  will  surely  not  gainsay  me  when  you  reflect 
that  I  have  made  only  a  limited  use  of  my  privilege  to 
weary  you.  I  could  have  taken  up  much  more  of 
your  time,  and  may,  therefore,  justly  close  with  Les- 
sing's  epigram  : 

"  If  thou  hast  found  in  all  these  pages  naught  that's  worth  the  thanks, 
At  least  have  gratitude  for  what  I've  spared  thee." 


THE  VELOCITY  OF  LIGHT. 


WHEN  a  criminal  judge  has  a  right  crafty  knave 
before  him,  one  well  versed  in  the  arts  of  pre- 
varication, his  main  object  is  to  wring  a  confession  from 
the  culprit  by  a  few  skilful  questions.  In  almost  a  simi- 
lar position  the  natural  philosopher  seems  to  be  placed 
with  respect  to  nature.  True,  his  functions  here  are 
more  those  of  the  spy  than  the  judge ;  but  his  object 
remains  pretty  much  the  same.  Her  hidden  motives 
and  laws  of  action  is  what  nature  must  be  made  to 
confess.  Whether  a  confession  will  be  extracted  de- 
pends upon  the  shrewdness  of  the  inquirer.  Not  with- 
out reason,  therefore,  did  Lord  Bacon  call  the  ex- 
perimental method  a  questioning  of  nature.  The 
art  consists  in  so  putting  our  questions  that  they 
may  not  remain  unanswered  without  a  breach  of  eti- 
quette. 

Look,  too,  at  the  countless  tools,  engines,  and  in- 
struments of  torture  with  which  man  conducts  his 
inquisitions  of  nature,  and  which  mock  the  poet's 
words  : 


THE  VELOCITY  OF  LIGHT.  49 

"  Mysterious  even  in  open  day, 
Nature  retains  her  veil,  despite  our  clamors  ; 
That  which  she  doth  not  willingly  display 
Cannot  be  wrenched  from  her  with  levers,  screws,  and  hammers." 

Look  at  these  instruments  and  you  will  see  that  the 
comparison  with  torture  also  is  admissible.* 

This  view  of  nature,  as  of  something  designedly 
concealed  from  man,  that  can  be  unveiled  only  by 
force  or  dishonesty,  chimed  in  better  with  the  concep- 
tions of  the  ancients  than  with  modern  notions.  A 
Grecian  philosopher  once  said,  in  offering  his  opinion 
of  the  natural  science  of  his  time,  that  it  could  only  be 
displeasing  to  the  gods  to  see  men  endeavoring  to  spy 
out  what  the  gods  were  not  minded  to  reveal  to  them.f 
Of  course  all  the  contemporaries  of  the  speaker  were 
not  of  his  opinion. 

Traces  of  this  view  may  still  be  found  to-day,  but 
upon  the  whole  we  are  now  not  so  narrow-minded. 
We  believe  no  longer  that  nature  designedly  hides 
herself.  We  know  now  from  the  history  of  science 
that  our  questions  are  sometimes  meaningless,  and 
that,  therefore,  no  answer  can  be  forthcoming.  Soon 
we  shall  see  how  man,  with  all  his  thoughts  and  quests, 
is  only  a  fragment  of  nature's  life. 

*  According  to  Mr.  Jules  Andrieu,  the  idea  that  nature  must  be  tortured 
to  reveal  her  secrets  is  preserved  in  the  name  crucible—  from  the  Latin  crux, 
a.  cross.  But,  more  probably,  crucible  is  derived  from  some  Old  French  or 
Teutonic  form,  as  crucke,  kroes,  krus,  etc.,  a  pot  or  jug  (cf.  Modorn  English 
crock,  cruse,  and  German  Krug). — Trans. 

t  Xenophon,  Memorabilia  iv,  7,  puts  into  the  mouth  of  Socrates  these 
words :  OVTE  yap  Evpera  avftpum>i£  avra  tv6pu£n  rival,  OVTS  xaoi&aticu 
deoif  av  f/yEiTo  rov  (.r/rovvra  a  EKEIVOI  oa<j>t/vtaai  ova 


5o  THE  VELOCITY  OF  LIGHT. 

Picture,  then,  as  your  fancy  dictates,  the  tools  oi 
the  physicist  as  instruments  of  torture  or  as  engines  of 
endearment,  at  all  events  a  chapter  from  the  history  of 
those  implements  will  be  of  interest  to  you,  and  it  will 
not  be  unpleasant  to  learn  what  were  the  peculiar  diffi- 
culties that  led  to  the  invention  of  such  strange  appa- 
ratus. 

Galileo  (born  at  Pisa  in  1564,  died  at  Arcetri  in 
1642)  was  the  first  who  asked  what  was  the  velocity 
of  light,  that  is,  what  time  it  would  take  for  a  light 
struck  at  one  place  to  become  visible  at  another,  a 
certain  distance  away.* 

The  method  which  Galileo  devised  was  as  simple 

as   it   was   natural.     Two   practised    observers,   with 

muffled  lanterns,  were  to  take  up  positions  in  a  dark 

night  at  a  considerable  dis- 

A B  tance  from  each  other,  one  at 

Fig.  13.  A  and  one  at  B.  At  a  moment 

previously  fixed  upon,  A  was 

instructed  to  unmask  his  lantern ;  while  as  soon  as  B 
saw  the  light  of  A's  lantern  he  was  to  unmask  his. 
Now  it  is  clear  that  the  time  which  A  counted  from 
the  uncovering  of  his  lantern  until  he  caught  sight  of 
the  light  of  £'s  would  be  the  time  which  it  would  take 
light  to  travel  from  A  to  B  and  from  B  back  to  A. 

The  experiment  was  not  executed,  nor  could  it,  in 
the  nature  of  the  case,  have  been  a  success.  As  we 


*  Galilei,  Discorsi  e  dimostrazione  matematiche.     Leyden,  1638.    Dialogo 


THE  VELOCITY  OF  LIGHT.  51 

now  know,  light  travels  too  rapidly  to  be  thus  noted. 
The  time  elapsing  between  the  arrival  of  the  light  at 
B  and  its  perception  by  the  observer,  with  that  be- 
tween the  decision  to  uncover  and  the  uncovering  of 
the  lantern,  is,  as  we  now  know,  incomparably  greater 
than  the  time  which  it  takes  light  to  travel  the  greatest 
earthly  distances.  The  great  velocity  of  light  will  be 
made  apparent,  if  we  reflect  that  a  flash  of  lightning 
in  the  night  illuminates  instantaneously  a  very  exten- 
sive region,  whilst  the  single  reflected  claps  of  thunder 
arrive  at  the  observer's  ear  very  gradually  and  in  ap- 
preciable succession. 

During  his  life,  then,  the  efforts  of  Galileo  to  de- 
termine the  velocity  of  light  remained  uncrowned  with 
success.  But  the  subsequent  history  of  the  measure- 
ment of  the  velocity  of  light  is  intimately  associated 
with  his  name,  for  with  the  telescope  which  he  con- 
structed he  discovered  the  four  satellites  of  Jupiter, 
and  these  furnished  the  next  occasion  for  the  deter- 
mination of  the  velocity  of  light. 

The  terrestrial  spaces  were  too  small  for  Galileo's 
experiment.  The  measurement  was  first  executed 
when  the  spaces  of  the  planetary  system  were  em- 
ployed. Olaf  Romer,  (born  at  Aarhuus  in  1644,  died 
at  Copenhagen  in  1710)  accomplished  the  feat  (1675- 
1676),  while  watching  with  Cassini  at  the  observatory 
of  Paris  the  revolutions  of  Jupiter's  moons. 

Let  AB  (Fig.  14)  be  Jupiter's  orbit.  Let  S  stand 
for  the  sun,  E  for  the  earth,  /for  Jupiter,  and  T for 


52  THE  VELOCITY  OF  LIGHT. 

Jupiter's  first  satellite.  When  the  earth  is  at  E^  we 
see  the  satellite  enter  regularly  into  Jupiter's  shadow, 
and  by  watching  the  time  between  two  successive 
eclipses,  can  calculate  its  time  of  revolution.  The 
time  which  Romer  noted  was  forty-two  hours,  twenty- 
eight  minutes,  and  thirty-five  seconds.  Now,  as  the 
earth  passes  along  in  its  orbit  towards  JE2,  the  revolu- 
tions of  the  satellite  grow  apparently  longer  and  longer  : 
1 


9 


/ 


Fig.  14. 

the  eclipses  take  place  later  and  later.  The  greatest 
retardation  of  the  eclipse,  which  occurs  when  the  earth 
is  at  Ez,  amounts  to  sixteen  minutes  and  twenty-six 
seconds.  As  the  earth  passes  back  again  to  Elt  the 
revolutions  grow  apparently  shorter,  and  they  occur 
in  exactly  the  time  that  they  first  did  when  the  earth 
arrives  at  E^ .  It  is  to  be  remarked  that  Jupiter  changes 
only  very  slightly  its  position  during  one  revolution  of 
the  earth.  Romer  guessed  at  once  that  these  period- 
ical changes  of  the  time  of  revolution  of  Jupiter's  satel- 


THE  VELOCITY  OF  LIGHT.  53 

lite  were  not  actual,  but  apparent  changes,  which  were 
in  some  way  connected  with  the  velocity  of  light. 

Let  us  make  this  matter  clear  to  ourselves  by  a  sim- 
ile. We  receive  regularly  by  the  post,  news  of  the 
political  status  at  our  capital.  However  far  away  we 
may  be  from  the  capital,  we  hear  the  news  of  every 
event,  later  it  is  true,  but  of  all  equally  late.  The 
events  reach  us  in  the  same  succession  of  time  as  that 
in  which  they  took  place.  But  if  we  are  travelling 
away  from  the  capital,  every  successive  post  will  have 
a  greater  distance  to  pass  over,  and  the  events  will 
reach  us  more  slowly  than  they  took  place.  The  re- 
verse will  be  the  case  if  we  are  approaching  the  capital. 

At  rest,  we  hear  a  piece  of  music  played  in  the 
same  tempo  at  all  distances.  But  the  tempo  will  be 
seemingly  accelerated  if  we  are  carried 
rapidly  towards  the  band,  or  retarded  if 
we  are  carried  rapidly  away  from  it.* 

Picture  to  yourself  a  cross,  say  the 
sails  of  a  wind-mill  (Fig.  15),  in  uniform  F»g-  »5- 

rotation  about  its  centre.  Clearly,  the  rotation  of  the 
cross  will  appear  to  you  more  slowly  executed  if  you 
are  carried  very  rapidly  away  from  it.  For  the  post 
which  in  this  case  conveys  to  you  the  light  and  brings 
to  you  the  news  of  the  successive  positions  of  the  cross 
will  have  to  travel  in  each  successive  instant  over  a 
longer  path. 

*In  the  same  way,  the  pitch  of  a  locomotive-whistle  is  higher  as  the 
locomotive  rapidly  approaches  an  observer,  and  lower  when  rapidly  leaving 
him  than  if  the  locomotive  were  at  rest. — Trans. 


54  THE  VELOCITY  OF  LIGHT. 

Now  this  must  also  be  the  case  with  the  rotation 
(the  revolution)  of  the  satellite  of  Jupiter.  The  great- 
est retardation  of  the  eclipse  (16^  minutes),  due  to 
the  passage  of  the  earth  from  £i  to  £2,  or  to  its  re- 
moval from  Jupiter  by  a  distance  equal  to  the  diameter 
of  the  orbit  of  the  earth,  plainly  corresponds  to  the 
time  which  it  takes  light  to  traverse  a  distance  equal  to 
the  diameter  of  the  earth's  orbit.  The  velocity  of  light, 
that  is,  the  distance  described  by  light  in  a  second,  as 
determined  by  this  calculation,  is  311,000  kilometres,* 
or  193,000  miles.  A  subsequent  correction  of  the  diam- 
eter of  the  earth's  orbit,  gives,  by  the  same  method, 
the  velocity  of  light  as  approximately  186,000  miles  a 
second. 

The  method  is  exactly  that  of  Galileo ;  only  better 
conditions  are  selected.  Instead  of  a  short  terrestrial 
distance  we  have  the  diameter  of  the  earth's  orbit, 
three  hundred  and  seven  million  kilometres ;  in  place 
of  the  uncovered  and  covered  lanterns  we  have  the 
satellite  of  Jupiter,  which  alternately  appears  and  dis- 
appears. Galileo,  therefore,  although  he  could  not 
carry  out  himself  the  proposed  measurement,  found 
the  lantern  by  which  it  was  ultimately  executed. 

Physicists  did  not  long  remain  satisfied  with  this 
beautiful  discovery.  They  sought  after  easier  meth- 
ods of  measuring  the  velocity  of  light,  such  as  might 
be  performed  on  the  earth.  This  was  possible  after  the 
difficulties  of  the  problem  were  clearly  exposed.  A 

*A  kilometre  is  0.621  or  nearly  five-eighths  of  a  statute  mile. 


THE  VELOCITY  OF  LIGHT.  55 

measurement  of  the  kind  referred  to  was  executed  in 
1849  by  Fizeau  (born  at  Paris  in  1819). 

I  shall  endeavor  to  make  the  principle  of  Fizeau's 
apparatus  clear  to  you.  Let  s  (Fig.  16)  be  a  disk  free 
to  rotate  about  its  centre,  and  perforated  at  its  rim 
with  a  series  of  holes.  Let  /  be  a  luminous  point 
casting  its  light  on  an  unsilvered  glass,  a,  inclined  at 
an  angle  of  forty-five  degrees  to  the  axis  of  the  disk. 
The  ray  of  light,  reflected  at  this  point,  passes  through 
one  of  the  holes  of  the  disk  and  falls  at  right  angles 


Fig.  16. 

upon  a  mirror  b,  erected  at  a  point  about  five  miles 
distant.  From  the  mirror  b  the  light  is  again  reflected, 
passes  once  more  through  the  hole  in  s,  and,  penetrat- 
ing the  glass  plate,  finally  strikes  the  eye,  o,  of  the  ob- 
server. The  eye,  o,  thus,  sees  the  image  of  the  lumi- 
nous point  /  through  the  glass  plate  and  the  hole  of 
the  disk  in  the  mirror  b. 

If,  now,  the  disk  be  set  in  rotation,  the  unpierced 
spaces  between  the  apertures  will  alternately  take  the 
place  of  the  apertures,  and  the  eye  o  will  now  see  the 
image  of  the  luminous  point  in  b  only  at  interrupted 
intervals.  On  increasing  the  rapidity  of  the  rotation, 


56  THE  VELOCITY  OF  LIGHT. 

however,  the  interruptions  for  the  eye  become  again 
unnoticeable,  and  the  eye  sees  the  mirror  b  uniformly 
illuminated. 

But  all  this  holds  true  only  for  relatively  small  ve- 
locities of  the  disk,  when  the  light  sent  through  an 
aperture  in  s  to  b  on  its  return  strikes  the  aperture  at 
almost  the  same  place  and  passes  through  it  a  second 
time.  Conceive,  now,  the  speed  of  the  disk  to  be  so  in- 
creased that  the  light  on  its  return  finds  before  it  an 
unpierced  space  instead  of  an  aperture,  it  will  then  no 
longer  be  able  to  reach  the  eye.  We  then  see  the 
mirror  b  only  when  no  light  is  emitted  from  it,  but 
only  when  light  is  sent  to  it ;  it  is  covered  when  light 
comes  from  it.  In  this  case,  accordingly,  the  mirror 
will  always  appear  dark. 

If  the  velocity  of  rotation  at  this  point  were  still 
further  increased,  the  light  sent  through  one  aperture 
could  not,  of  course,  on  its  return  pass  through  the 
same  aperture  but  might  strike  the  next  and  reach 
the  eye  by  that.  Hence,  by  constantly  increasing  the 
velocity  of  the  rotation,  the  mirror  b  may  be  made  to 
appear  alternately  bright  and  dark.  Plainly,  now,  if 
we  know  the  number  of  apertures  of  the  disk,  the  num- 
ber of  rotations  per  second,  and  the  distance  sb,  we 
can  calculate  the  velocity  of  light.  The  result  agrees 
with  that  obtained  by  Romer. 

The  experiment  is  not  quite  as  simple  as  my  ex- 
position might  lead  you  to  believe.  Care  must  be 
taken  that  the  light  shall  travel  back  and  forth  over 


THE  VELOCITY  OF  LIGHT.  57 

the  miles  of  distance  sb  and  bs  tmdispersed.  This 
difficulty  is  obviated  by  means  of  telescopes. 

If  we  examine  Fizeau's  apparatus  closely,  we  shall 
recognise  in  it  an  old  acquaintance  :  the  arrangement 
of  Galileo's  experiment.  The  luminous  point  /  is  the 
lantern  A,  while  the  rotation  of  the  perforated  disk  per- 
forms mechanically  the  uncovering  and  covering  of  the 
lantern.  Instead  of  the  unskilful  observer  B  we  have 
the  mirror  b,  which  is  unfailingly  illuminated  the  instant 
the  light  arrives  from  s.  The  disk  s,  by  alternately 
transmitting  and  intercepting  the  reflected  light, assists 
the  observer  o.  Galileo's  experiment  is  here  executed, 
so  to  speak,  countless  times  in  a  second,  yet  the  total 
result  admits  of  actual  observation.  If  I  might  be 
pardoned  the  use  of  a  phrase  of  Darwin's  in  this  field, 
I  should  say  that  Fizeau's  apparatus  was  the  descen- 
dant of  Galileo's  lantern. 

A  still  more  refined  and  delicate  method  for  the 
measurement  of  the  velocity  of  light  was  employed  by 
Foucault,  but  a  description  of  it  here  would  lead  us 
too  far  from  our  subject. 

The  measurement  of  the  velocity  of  sound  is  easily 
executed  by  the  method  of  Galileo.  It  was  unneces- 
sary, therefore,  for  physicists  to  rack  their  brains  fur- 
ther about  the  matter  ;  but  the  idea  which  with  light 
grew  out  of  necessity  was  applied  also  in  this  field. 
Koenig  of  Paris  constructs  an  apparatus  for  the  meas- 
urement of  the  velocity  of  sound  which  is  closely  allied 
to  the  method  of  Fizeau. 


58  THE  VELOCITY  OF  LIGHT. 

The  apparatus  is  very  simple.  It  consists  of  two 
electrical  clock-works  which  strike  simultaneously, 
with  perfect  precision,  tenths  of  seconds.  If  we  place 
the  two  clock-works  directly  side  by  side,  we  hear 
their  strokes  simultaneously,  wherever  we  stand.  But 
if  we  take  our  stand  by  the  side  of  one  of  the  works 
and  place  the  other  at  some  distance  from  us,  in  gen- 
eral a  coincidence  of  the  strokes  will  now  not  be  heard. 
The  companion  strokes  of  the  remote  clock-work  ar- 
rive, as  sound,  later.  The  first  stroke  of  the  remote 
work  is  heard,  for  example,  immediately  after  the  first 
of  the  adjacent  work,  and  so  on.  But  by  increasing 
the  distance  we  may  produce  again  a  coincidence  of  the 
strokes.  For  example,  the  first  stroke  of  the  remote 
work  coincides  with  the  second  of  the  near  work,  the 
second  of  the  remote  work  with  the  third  of  the  near 
work,  and  so  on.  If,  now,  the  works  strike  tenths  of 
seconds  and  the  distance  between  them  is  increased 
until  the  first  coincidence  is  noted,  plainly  that  dis- 
tance is  travelled  over  by  the  sound  in  a  tenth  of  a 
second. 

We  meet  frequently  the  phenomenon  here  pre- 
sented, that  a  thought  which  centuries  of  slow  and 
painful  endeavor  are  necessary  to  produce,  when  once 
developed,  fairly  thrives.  It  spreads  and  runs  every- 
where, even  entering  minds  in  which  it  could  never 
have  arisen.  It  simply  cannot  be  eradicated. 

The  determination  of  the  velocity  of  light  is  not  the 
only  case  in  which  the  direct  perception  of  the  senses 


THE  VELOCITY  OF  LIGHT.  59 

is  too  slow  and  clumsy  for  use.  The  usual  method 
of  studying  events  too  fleet  for  direct  observation  con- 
sists in  putting  into  reciprocal  action  with  them  other 
events  already  known,  the  velocities  of  all  of  which 
are  capable  of  comparison.  The  result  is 
usually  unmistakable,  and  susceptible  of 
direct  inference  respecting  the  character  of 
the  event  which  is  unknown.  The  velocity 
of  electricity  cannot  be  determined  by  di- 
rect observation.  But  it  was  ascertained 
by  Wheatstone,  simply  by  the  expedient  of 
watching  an  electric  spark  in  a  mirror  rotating  with 
tremendous  known  velocity. 

If  we  wave  a  staff  irregularly  hither  and  thither, 
simple  observation  cannot  determine  how  quickly  it 
moves  at  each  point  of  its  course.  But  let  us  look  at 
the  staff  through  holes  in  the  rim  of  a 
rapidly  rotating  disk  (Fig.  17).  We 
shall  then  see  the  moving  staff  only 
in  certain  positions,  namely,  when  a 
hole  passes  in  front  of  the  eye.  The 
single  pictures  of  the  staff  remain  for  a  Flg>  l8' 

time  impressed  upon  the  eye  ;  we  think  we  see  several 
staffs,  having  some  such  disposition  as  that  represented 
in  Fig.  1 8.  If,  now,  the  holes  of  the  disk  are  equally 
far  apart,  and  the  disk  is  rotated  with  uniform  velo- 
city, we  see  clearly  that  the  staff  has  moved  slowly 
from  a  to  b,  more  quickly  from  b  to  <r,  still  more  quickly 
from  c  to  d,  and  with  its  greatest  velocity  from  d  to  e. 


60  THE  VELOCITY  OF  LIGHT. 

A  jet  of  water  flowing  from  an  orifice  in  the  bottom 
of  a  vessel  has  the  appearance  of  perfect  quiet  and 
uniformity,  but  if  we  illuminate  it  for  a  second,  in  a 
dark  room,  by  means  of  an  electric  flash  we  shall  see 
that  the  jet  is  composed  of  separate  drops.  By  their 
quick  descent  the  images  of  the  drops  are 


10 
.20 
30 
40 
50 


obliterated  and  the  jet  appears  uniform. 
Let  us  look  at  the  jet  through  the  rotating 
disk.  The  disk  is  supposed  to  be  rotated  so 
rapidly  that  while  the  second  aperture 


Fig.  19.  passes  into  the  place  of  the  first,  drop  i 
falls  into  the  place  of  2,  2  into  the  place  of  3,  and  so  on. 
We  see  drops  then  always  in  the  same  places.  The 
jet  appears  to  be  at  rest.  If  we  turn  the  disk  a  trifle 
more  slowly,  then  while  the  second  aperture  passes 
into  the  place  of  the  first,  drop  i  will  have  fallen  some- 
what lower  than  2,  2  somewhat  lower  than  3,  etc. 
Through  every  successive  aperture  we  shall  see  drops 
in  successively  lower  positions.  The  jet  will  appear  to 
be  flowing  slowly  downwards. 

Now  let  us  turn  the  disk  more  rapidly.  Then  while 
the  second  aperture  is  passing  into  the  place  of  the 
first,  drop  i  will  not  quite  have  reached  the  place  of  2, 
but  will  be  found  slightly  above  2,  2  slightly  above  3, 
etc.  Through  the  successive  apertures  we  shall  see 
the  drops  at  successively  higher  places.  It  will  now 
look  as  if  the  jet  were  flowing  upwards,  as  if  the  drops 
were  rising  from  the  lower  vessel  into  the  higher. 

You  see,  physics  grows  gradually  more  and  more 


THE  VELOCITY  OF  LIGHT.  61 

terrible.  The  physicist  will  soon  have  it  in  his  power 
to  play  the  part  of  the  famous  lobster  chained  to  the 
bottom  of  the  Lake  of  Mohrin,  whose  direful  mission, 
if  ever  liberated,  the  poet  Kopisch  humorously  de- 
scribes as  that  of  a  reversal  of  all  the  events  of  the 
world  ;  the  rafters  of  houses  become  trees  again,  cows 
calves,  honey  flowers,  chickens  eggs,  and  the  poet's 
own  poem  flows  back  into  his  inkstand. 

* 
*  * 

You  will  now  allow  me  the  privilege  of  a  few  gen- 
eral remarks.  You  have  seen  that  the  same  principle 
often  lies  at  the  basis  of  large  classes  of  apparatus 
designed  for  different  purposes.  Frequently  it  is  some 
very  unobtrusive  idea  which  is  productive  of  so  much 
fruit  and  of  such  extensive  transformations  in  physical 
technics.  It  is  not  otherwise  here  than  in  practical 
life. 

The  wheel  of  a  waggon  appears  to  us  a  very  simple 
and  insignificant  creation.  But  its  inventor  was  cer- 
tainly a  man  of  genius.  The  round  trunk  of  a  tree 
perhaps  first  accidentally  led  to  the  observation  of  the 
ease  with  which  a  load  can  be  moved  on  a  roller. 
Now,  the  step  from  a  simple  supporting  roller  to  a 
fixed  roller,  or  wheel,  appears  a  very  easy  one.  At 
least  it  appears  very  easy  to  us  who  are  accustomed 
from  childhood  up  to  the  action  of  the  wheel.  But  if 
we  put  ourselves  vividly  into  the  position  of  a  man 
who  never  saw  a  wheel,  but  had  to  invent  one,  we  shall 
begin  to  have  some  idea  of  its  difficulties.  Indeed,  it 


62  THE  VELOCITY  OF  LIGHT. 

is  even  doubtful  whether  a  single  man  could  have  ac- 
complished this  feat,  whether  perhaps  centuries  were 
not  necessary  to  form  the  first  wheel  from  the  primi- 
tive roller.* 

History  does  not  name  the  progressive  minds  who 
constructed  the  first  wheel ;  their  time  lies  far  back  of 
the  historic  period.  No  scientific  academy  crowned 
their  efforts,  no  society  of  engineers  elected  them 
honorary  members.  They  still  live  only  in  the  stu- 
pendous results  which  they  called  forth.  Take  from 
us  the  wheel,  and  little  will  remain  of  the  arts  and  in- 
dustries of  modern  life.  All  disappears.  From  the 
spinning-wheel  to  the  spinning- mill,  from  the  turning- 
lathe  to  the  rolling-mill,  from  the  wheelbarrow  to  the 
railway  train,  all  vanishes. 

In  science  the  wheel  is  equally  important.  Whirl- 
ing machines,  as  the  simplest  means  of  obtaining  quick 
motions  with  inconsiderable  changes  of  place,  play  a 
part  in  all  branches  of  physics.  You  know  Wheat- 
stone's  rotating  mirror,  Fizeau's  wheel,  Plateau's  per- 
forated rotating  disks,  etc.  Almost  the  same  principle 
lies  at  the  basis  of  all  these  apparatus.  They  differ 
from  one  another  no  more  than  the  pen-knife  differs, 
in  the  purposes  it  serves,  from  the  knife  of  the  anato- 
mist or  the  knife  of  the  vine-dresser.  Almost  the  same 
might  be  said  of  the  screw. 

*  Observe,  also,  the  respect  in  which  the  wheel  is  held  in  India,  Japan 
and  other  Buddhistic  countries,  as  the  emblem  of  power,  order,  and  law,  and 
of  the  superiority  of  mind  over  matter.  The  consciousness  of  the  importance  of 
this  invention  seems  to  have  lingered  long  in  the  minds  of  these  nations. — Tr. 


THE  VELOCITY  OF  LIGHT.  63 

It  will  now  perhaps  be  clear  to  you  that  new 
thoughts  do  not  spring  up  suddenly.  Thoughts  need 
their  time  to  ripen,  grow,  and  develop  in,  like  every 
natural  product ;  for  man,  with  his  thoughts,  is  also  a 
part  of  nature. 

Slowly,  gradually,  and  laboriously  one  thought  is 
transformed  into  a  different  thought,  as  in  all  likelihood 
one  animal  species  is  gradually  transformed  into  new 
species.  Many  ideas  arise  simultaneously.  They  fight 
the  battle  for  existence  not  otherwise  than  do  the 
Ichthyosaurus,  the  Brahman,  and  the  horse. 

A  few  remain  to  spread  rapidly  over  all  fields  of 
knowledge,  to  be  redeveloped,  to  be  again  split  up,  to 
begin  again  the  struggle  from  the  start.  As  many 
animal  species  long  since  conquered,  the  relicts  of 
ages  past,  still  live  in  remote  regions  where  their  ene- 
mies cannot  reach  them,  so  also  we  find  conquered 
ideas  still  living  on  in  the  minds  of  many  men.  Who- 
ever will  look  carefully  into  his  own  soul  will  acknowl- 
edge that  thoughts  battle  as  obstinately  for  existence 
as  animals.  Who  will  gainsay  that  many  vanquished 
modes  of  thought  still  haunt  obscure  crannies  of  his 
brain,  too  faint-hearted  to  step  out  into  the  clear  light 
of  reason  ?  What  inquirer  does  not  know  that  the 
hardest  battle,  in  the  transformation  of  his  ideas,  is 
fought  with  himself. 

Similar  phenomena  meet  the  natural  inquirer  in  all 
paths  and  in  the  most  trifling  matters.  The  true  in- 
quirer seeks  the  truth  everywhere,  in  his  country- 


64  THE  VELOCITY  OF  LIGHT. 

walks  and  on  the  streets  of  the  great  city.  If  he  is 
not  too  learned,  he  will  observe  that  certain  things, 
like  ladies'  hats,  are  constantly  subject  to  change.  I 
have  not  pursued  special  studies  on  this  subject,  but 
as  long  as  I  can  remember,  one  form  has  always 
gradually  changed  into  another.  First,  they  wore  hats 
with  long  projecting  rims,  within  which,  scarcely  ac- 
cessible with  a  telescope,  lay  concealed  the  face  of  the 
beautiful  wearer.  The  rim  grew  smaller  and  smaller; 
the  bonnet  shrank  to  the  irony  of  a  hat.  Now  a  tre- 
mendous superstructure  is  beginning  to  grow  up  in  its 
place,  and  the  gods  only  know  what  its  limits  will  be. 
It  is  not  otherwise  with  ladies'  hats  than  with  butter- 
flies, whose  multiplicity  of  form  often  simply  comes 
from  a  slight  excrescence  on  the  wing  of  one  species 
developing  in  a  cognate  species  to  a  tremendous  fold. 
Nature,  too,  has  its  fashions,  but  they  last  thousands 
of  years.  I  could  elucidate  this  idea  by  many  addi- 
tional examples;  for  instance,  by  the  history  of  the 
evolution  of  the  coat,  if  I  were  not  fearful  that  my 
gossip  might  prove  irksome  to  you. 

* 
*  * 

We  have  now  wandered  through  an  odd  corner  of 
the  history  of  science.  What  have  we  learned  ?  The 
solution  of  a  small,  I  might  almost  say  insignificant, 
problem — the  measurement  of  the  velocity  of  light. 
And  more  than  two  centuries  have  worked  at  its  solu- 
tion !  Three  of  the  most  eminent  natural  philosophers, 
Galileo,  an  Italian,  Romer,  a  Dane,  and  Fizeau,  a 


THE  VELOCITY  OF  LIGHT.  65 

Frenchman,  have  fairly  shared  its  labors.  And  so  it 
is  with  countless  other  questions.  When  we  contem- 
plate thus  the  many  blossoms  of  thought  that  must 
wither  and  fall  before  one  shall  bloom,  then  shall  we 
first  truly  appreciate  Christ's  weighty  but  little  con- 
solatory words  :  "  Many  be  called  but  few  are  chosen. " 

Such  is  the  testimony  of  every  page  of  history. 
But  is  history  right?  Are  really  only  those  chosen 
whom  she  names  ?  Have  those  lived  and  battled  in 
vain,  who  have  won  no  prize? 

I  doubt  it.  And  so  will  every  one  who  has  felt  the 
pangs  of  sleepless  nights  spent  in  thought,  at  first  fruit- 
less, but  in  the  end  successful.  No  thought  in  such 
struggles  was  thought  in  vain  ;  each  one,  even  the  most 
insignificant,  nay,  even  the  erroneous  thought,  that 
which  apparently  was  the  least  productive,  served  to 
prepare  the  way  for  those  that  afterwards  bore  fruit. 
And  as  in  the  thought  of  the  individual  naught  is  in 
vain,  so,  also,  it  is  in  that  of  humanity. 

Galileo  wished  to  measure  the  velocity  of  light. 
He  had  to  close  his  eyes  before  his  wish  was  realised. 
But  he  at  least  found  the  lantern  by  which  his  succes- 
sor could  accomplish  the  task. 

And  so  I  may  maintain  that  we  all,  so  far  as  inclina- 
tion goes,  are  working  at  the  civilisation  of  the  future. 
If  only  we  all  strive  for  the  right,  then  are  we  all 
called  and  all  chosen  ! 


WHY  HAS  MAN  TWO  EYES  ? 


WHY  has  man  two  eyes  ?  That  the  pretty  sym- 
metry of  his  face  may  not  be  disturbed,  the 
artist  answers.  That  his  second  eye  may  furnish  a 
substitute  for  his  first  if  that  be  lost,  says  the  far- 
sighted  economist.  That  we  may  weep  with  two  eyes 
at  the  sins  of  the  world,  replies  the  religious  enthu- 
siast. 

Odd  opinions  !  Yet  if  you  should  approach  a  mod- 
ern scientist  with  this  question  you  might  consider 
yourself  fortunate  if  you  escaped  with  less  than  a  re- 
buff. "  Pardon  me,  madam,  or  my  dear  sir,"  he  would 
say,  with  stern  expression,  "man  fulfils  no  purpose  in 
the  possession  of  his  eyes  ;  nature  is  not  a  person,  and 
consequently  not  so  vulgar  as  to  pursue  purposes  of 
any  kind." 

Still  an  unsatisfactory  answer  !  I  once  knew  a  pro- 
fessor who  would  shut  with  horror  the  mouths  of  his 
pupils  if  they  put  to  him  such  an  unscientific  question. 

But  ask  a  more  tolerant  person,  ask  me.  I,  I  can- 
didly confess,  do  not  know  exactly  why  man  has  two 


WHY  HAS  MAN  TWO  EYES?  67 

eyes,  but  the  reason  partly  is,  I  think,  that  I  may  see 
you  here  before  me  to-night  and  talk  with  you  upon 
this  delightful  subject. 

Again  you  smile  incredulously.  Now  this  is  one  of 
those  questions  that  a  hundred  wise  men  together 
could  not  answer.  You  have  heard,  so  far,  only  five  of 
these  wise  men.  You  will  certainly  want  to  be  spared 
the  opinions  of  the  other  ninety-five.  To  the  first  you 
will  reply  that  we  should  look  just  as  pretty  if  we  were 
born  with  only  one  eye,  like  the  Cyclops ;  to  the  sec- 
ond we  should  be  much  better  off,  according  to  his 
principle,  if  we  had  four  or  eight  eyes,  and  that  in  this 
respect  we  are  vastly  inferior  to  spiders  ;  to  the  third, 
that  you  are  not  just  in  the  mood  to  weep ;  to  the 
fourth,  that  the  unqualified  interdiction  of  the  question 
excites  rather  than  satisfies  your  curiosity ;  while  of 
me  you  will  dispose  by  saying  that  my  pleasure  is  not 
as  intense  as  I  think,  and  certainly  not  great  enough 
to  justify  the  existence  of  a  double  eye  in  man  since 
the  fall  of  Adam. 

But  since  you  are  not  satisfied  with  my  brief  and 
obvious  answer,  you  have  only  yourselves  to  blame 
for  the  consequences.  You  must  now  listen  to  a  longer 
and  more  learned  explanation,  such  as  it  is  in  my 
power  to  give. 

As  the  church  of  science,  however,  debars  the  ques- 
tion "Why?  "  let  us  put  the  matter  in  a  purely  ortho- 
dox way :  Man  has  two  eyes,  what  more  can  he  see  with 
two  than  with  one? 


68 


WHY  HAS  MAN  TWO  EYES? 


I  will  invite  you  to  take  a  walk  with  me  ?  We  see 
before  us  a  wood.  What  is  it  that  makes  this  real 
wood  contrast  so  favorably  with  a  painted  wood,  no 
matter  how  perfect  the  painting  may  be?  What  makes 
the  one  so  much  more  lovely  than  the  other?  Is  it  the 
vividness  of  the  coloring,  the  distribution  of  the  lights 
and  the  shadows?  I  think 
not.  On  the  contrary,  it 
seems  to  me  that  in  this 
respect  painting  can  ac- 
complish very  much. 

The  cunning  hand  of 
the  painter  can  conjure  up 
with  a  few  strokes  of  his 
brush  forms  of  wonderful 
plasticity.  By  the  help  of 
other  means  even  more 
can  be  attained.  Photo- 
graphs of  reliefs  are  so 
plastic  that  we  often  im- 
agine we  can  actually  lay 
hold  of  the  elevations  and 
depressions. 

But  one  thing  the  painter  never  can  give  with  the 
vividness  that  nature  does — the  difference  of  near  and 
far.  In  the  real  woods  you  see  plainly  that  you  can 
lay  hold  of  some  trees,  but  that  others  are  inaccessibly 
far.  The  picture  of  the  painter  is  rigid.  The  picture 
of  the  real  woods  changes  on  the  slightest  movement. 


WHY  HAS  MAN  TWO  EYES?  69 

Now  this  branch  is  hidden  behind  that ;  now  that  be- 
hind this.  The  trees  are  alternately  visible  and  in- 
visible. 

Let  us  look  at  this  matter  a  little  more  closely. 
For  convenience  sake  we  shall  remain  upon  the  high- 
way, I,  II.  (Fig.  20.)  To  the  right  and  the  left  lies  the 
forest.  Standing  at  I,  we  see,  let  us  say,  three  trees 
(i,  2,  3)  in  a  line,  so  that  the  two  remote  ones  are 
covered  by  the  nearest.  Moving  further  along,  this 
changes.  At  II  we  shall  not  have  to  look  round  so  far 
to  see  the  remotest  tree  3  as  to  see  the  nearer  tree  2, 
nor  so  far  to  see  this  as  to  see  i.  Hence,  as  we  move 
onward,  objects  that  are  near  to  us  seem  to  lag  behind  as 
compared  with  objects  that  are  remote  from  us,  the  lagging 
increasing  with  the  proximity  of  the  objects.  Very  remote 
objects,  towards  which  we  must  always  look  in  the 
same  direction  as  we  proceed,  appear  to  travel  along 
with  us. 

If  we  should  see,  therefore,  jutting  above  the  brow 
of  yonder  hill  the  tops  of  two  trees  whose  distance 
from  us  we  were  in  doubt  about,  we  should  have  in 
our  hands  a  very  easy  means  of  deciding  the  question. 
We  should  take  a  few  steps  forward,  say  to  the  right, 
and  the  tree-top  which  receded  most  to  the  left  would 
be  the  one  nearer  to  us.  In  truth,  from  the  amount 
of  the  recession  a  geometer  could  actually  determine 
the  distance  of  the  trees  from  us  without  ever  going 
near  them.  It  is  simply  the  scientific  development  of 


70  WHY  HAS  MAN  TWO  EYES? 

this  perception  that  enables  us  to  measure  the  distances 
of  the  stars. 

Hence,  from  change  of  view  in  forward  motion  the 
distances  of  objects  in  our  field  of  vision  can  be  measured. 

Rigorously,  however,  even  forward  motion  is  not 
necessary.  For  every  observer  is  composed  really  of 
two  observers.  Man  has  two  eyes.  The  right  eye  is 
a  short  step  ahead  of  the  left  eye  in  the  right-hand  di- 
rection. Hence,  the  two  eyes  receive  different  pic- 
tures of  the  same  woods.  The  right  eye  will  see  the 
near  trees  displaced  to  the  left,  and  the  left  eye  will 
see  them  displaced  to  the  right,  the  displacement  being 
greater,  the  greater  the  proximity.  This  difference  is 
sufficient  for  forming  ideas  of  distance. 

We  may  now  readily  convince  ourselves  of  the  fol- 
lowing facts : 

1.  With  one  eye,  the  other  being  shut,  you  have  a 
very  uncertain  judgment  of  distances.     You  will  find 
it,  for  example,  no  easy  task,  with  one  eye  shut,  to 
thrust  a  stick  through  a  ring  hung  up  before  you;  you 
will  miss  the  ring  in  almost  every  instance. 

2.  You  see  the  same  object  differently  with  the 
right  eye  from  what  you  do  with  the  left. 

Place  a  lamp-shade  on  the  table  in  front  of  you 
with  its  broad  opening  turned  downwards,  and  look 
at  it  from  above.  (Fig.  21.)  You  will  see  with  your 
right  eye  the  image  2,  with  your  left  eye  the  image  i. 
Again,  place  the  shade  with  its  wide  opening  turned 
upwards;  you  will  receive  with  your  right  eye  the  im- 


WHY  HAS  MAN  TWO  EYES?  71 

age  4,  with  your  left  eye  the  image  3.    Euclid  mentions 
phenomena  of  this  character. 

3.  Finally,  you  know  that  it  is  easy  to  judge  of 
distances  with  both  eyes.  Accordingly  your  judgment 
must  spring  in  some  way  from  a  co-operation  of  the 

1  2 


Fig.  21. 

two  eyes.  In  the  preceding  example  the  openings  in 
the  different  images  received  by  the  two  eyes  seem 
displaced  with  respect  to  one  another,  and  this  dis- 
placement is  sufficient  for  the  inference  that  the  one 
opening  is  nearer  than  the  other. 

I  have  no  doubt  that  you,  ladies,  have  frequently 
received  delicate  compliments  upon  your  eyes,  but   I 


72  WHY  HAS  MAN  TWO  EYES  ? 

feel  sure  that  no  one  has  ever  told  you,  and  I  know  not 
whether  it  will  flatter  you,  that  you  have  in  your  eyes, 
be  they  blue  or  black,  little  geometricians.  You  say 
you  know  nothing  of  them?  Well,  for  that  matter, 
neither  do  I.  But  the  facts  are  as  I  tell  you. 

You  understand  little  of  geometry?  I  shall  accept 
that  confession.  Yet  with  the  help  of  your  two  eyes 
you  judge  of  distances?  Surely  that  is  a  geometrical 
problem.  And  what  is  more,  you  know  the  solution 
of  this  problem  :  for  you  estimate  distances  correctly. 
If,  then,  you  do  not  solve  the  problem,  the  little  geom- 
etricians in  your  eyes  must  do  it  clandestinely  and  whis- 
per the  solution  to  you.  I  doubt  not  they  are  fleet  little 
fellows. 

What  amazes  me  most  here  is,  that  you  know  noth- 
ing about  these  little  geometricians.  But  perhaps  they 
also  know  nothing  about  you.  Perhaps  they  are  mod- 
els of  punctuality,  routine  clerks  who  bother  about 
nothing  but  their  fixed  work.  In  that  case  we  may 
be  able  to  deceive  the  gentlemen. 

If  we  present  to  our  right  eye  an  image  which  looks 
exactly  like  the  lamp-shade  for  the  right  eye,  and  to 
our  left  eye  an  image  which  looks  exactly  like  a  lamp- 
shade for  the  left  eye,  we  shall  imagine  that  we  see 
the  whole  lamp-shade  bodily  before  us. 

You  know  the  experiment.  If  you  are  practised  in 
squinting,  you  can  perform  it  directly  with  the  figure, 
looking  with  your  right  eye  at  the  right  image,  and 
with  your  left  eye  at  the  left  image.  In  this  way  the 


WHY  HAS  MAN  7WO  EYES?  73 

experiment  was  first  performed  by  Elliott.  Improved 
and  perfected,  its  form  is  Wheatstone's  stereoscope, 
made  so  popular  and  useful  by  Brewster. 

By  taking  two  photographs  of  the  same  object  from 
two  different  points,  corresponding  to  the  two  eyes,  a 
very  clear  three-dimensional  picture  of  distant  places 
or  buildings  can  be  produced  by  the  stereoscope. 

But  the  stereoscope  accomplishes  still  more  than 
this.  It  can  visualise  things  for  us  which  we  never  see 
with  equal  clearness  in  real  objects.  You  know  that 
if  you  move  much  while  your  photograph  is  being 
taken,  your  picture  will  come  out  like  that  of  a  Hindu 
deity,  with  several  heads  or  several  arms,  which,  at 
the  spaces  where  they  overlap,  show  forth  with  equal 
distinctness,  so  that  we  seem  to  see  the  one  picture 
through  the  other.  If  a  person  moves  quickly  away 
from  the  camera  before  the  impression  is  completed, 
the  objects  behind  him  will  also  be  imprinted  upon 
the  photograph;  the  person  will  look  transparent. 
Photographic  ghosts  are  made  in  this  way. 

Some  very  useful  applications  may  be  made  of  this 
discovery.  For  example,  if  we  photograph  a  machine 
stereoscopically,  successively  removing  during  the 
operation  the  single  parts  (where  of  course  the  im- 
pression suffers  interruptions),  we  obtain  a  transparent 
view,  endowed  with  all  the  marks  of  spatial  solidity, 
in  which  is  distinctly  visualised  the  interaction  of  parts 
normally  concealed.  I  have  employed  this  method  for 


74  WHY  HAS  MAN  7^  WO  EYES  ? 

obtaining  transparent  stereoscopic  views  of  anatom- 
ical structures. 

You  see,  photography  is  making  stupendous  ad- 
vances, and  there  is  great  danger  that  in  time  some 
malicious  artist  will  photograph  his  innocent  patrons 
with  solid  views  of  their  most  secret  thoughts  and 
emotions.  How  tranquil  politics  will  then  be  !  What 
rich  harvests  our  detective  force  will  reap  ! 

* 
*  * 

By  the  joint  action  of  the  two  eyes,  therefore,  we 
arrive  at  our  judgments  of  distances,  as  also  of  the 
forms  of  bodies. 

Permit  me  to  mention  here  a  few  additional  facts 
connected  with  this  subject,  which  will  assist  us  in  the 
comprehension  of  certain  phenomena  in  the  history  of 
civilisation. 

You  have  often  heard,  and  know  from  personal  ex- 
perience, that  remote  objects  appear  perspectively 
dwarfed.  In  fact,  it  is  easy  to  satisfy  yourself  that 
you  can  cover  the  image  of  a  man  a  few  feet  away 
from  you  simply  by  holding  up  your  finger  a  short  dis- 
tance in  front  of  your  eye.  Still,  as  a  general  rule, 
you  do  not  notice  this  shrinkage  of  objects.  On  the 
contrary,  you  imagine  you  see  a  man  at  the  end  of  a 
large  hall,  as  large  as  you  see  him  near  by  you.  For 
your  eye,  in  its  measurement  of  the  distances,  makes 
remote  objects  correspondingly  larger.  The  eye,  so  to 
speak,  is  aware  of  this  perspective  contraction  and  is 
not  deceived  by  it,  although  its  possessor  is  unconscious 


WHY  HAS  MAN  TWO  EYES?  75 

of  the  fact.  All  persons  who  have  attempted  to  draw 
from  nature  have  vividly  felt  the  difficulty  which  this 
superior  dexterity  of  the  eye  causes  the  perspective 
conception.  Not  until  one's  judgment  of  distances  it> 
made  uncertain,  by  their  size,  or  from  lack  of  points 
of  reference,  or  from  being  too  quickly  changed,  is  the 
perspective  rendered  very  prominent. 

On  sweeping  round  a  curve  on  a  rapidly  moving 
railway  train,  where  a  wide  prospect  is  suddenly 
opened  up,  the  men  upon  distant  hills  appear  like 
dolls.*  You  have  at  the  moment,  here,  no  known 
references  for  the  measurement  of  distances.  The 
stones  at  the  entrance  of  a  tunnel  grow  visibly  larger 
as  we  ride  towards  it ;  they  shrink  visibly  in  size  as  we 
ride  from  it. 

Usually  both  eyes  work  together.  As  certain  views 
are  frequently  repeated,  and  lead  always  to  substan- 
tially the  same  judgments  of  distances,  the  eyes  in 
time  must  acquire  a  special  skill  in  geometrical  con- 
structions. In  the  end,  undoubtedly,  this  skill  is  so 
increased  that  a  single  eye  alone  is  often  tempted  to 
exercise  that  office. 

Permit  me  to  elucidate  this  point  by  an  example. 
Is  any  sight  more  familiar  to  you  than  that  of  a  vista 
down  a  long  street?  Who  has  not  looked  with  hopeful 


•This  effect  is  particularly  noticeable  in  the  size  of  workmen  on  high 
chimneys  and  church-steeples— "  steeple  Jacks."  When  the  cables  were  slung 
from  the  towers  of  the  Brooklyn  bridge  (277  feet  high),  the  men  sent  out  in 
baskets  to  paint  them,  appeared,  against  the  broad  background  of  heaven  and 
water,  like  flies.—  Trans. 


76  WHY  HAS  MAN-  TWO  EYES? 

eyes  time  and  again  into  a  street  and  measured  its 
depth.  I  will  take  you  now  into  an  art-gallery  where 
I  will  suppose  you  to  see  a  picture  representing  a  vista 
into  a  street.  The  artist  has  not  spared  his  rulers  to 
get  his  perspective  perfect.  The  geometrician  in  your 
left  eye  thinks,  "Ah  ha  !  I  have  computed  that  case  a 
hundred  times  or  more.  I  know  it  by  heart.  It  is  a 
vista  into  a  street,"  he  continues  ;  "  where  the  houses 
are  lower  is  the  remote  end."  The  geometrician  in 
the  right  eye,  too  much  at  his  ease  to  question  his 
possibly  peevish  comrade  in  the  matter,  answers  the 
same.  But  the  sense  of  duty  of  these  punctual  little 
fellows  is  at  once  rearoused.  They  set  to  work  at  their 
calculations  and  immediately  find  that  all  the  points 
of  the  picture  are  equally  distant  from  them,  that  is, 
lie  all  upon  a  plane  surface. 

What  opinion  will  you  now  accept,  the  first  or  the 
second  ?  If  you  accept  the  first  you  will  see  distinctly 
the  vista.  If  you  accept  the  second  you  will  see  noth- 
ing but  a  painted  sheet  of  distorted  images. 

It  seems  to  you  a  trifling  matter  to  look  at  a  pic- 
ture and  understand  its  perspective.  Yet  centuries 
elapsed  before  humanity  came  fully  to  appreciate  this 
trifle,  and  even  the  majority  of  you  first  learned  it  from 
education. 

I  can  remember  very  distinctly  that  at  three  years 
of  age  all  perspective  drawings  appeared  to  me  as 
gross  caricatures  of  objects.  I  could  not  understand 
why  artists  made  tables  so  broad  at  one  end  and  so 


WHY  HAS  MAN  TWO  E  YES  f  77 

narrow  at  the  other.  Real  tables  seemed  to  me  just 
as  broad  at  one  end  as  at  the  other,  because  my  eye 
made  and  interpreted  its  calculations  without  my  in- 
tervention. But  that  the  picture  of  the  table  on  the 
plane  surface  was  not  to  be  conceived  as  a  plane  painted 
surface  but  stood  for  a  table  and  so  was  to  be  imaged 
with  all  the  attributes  of  extension  was  a  joke  that  I 
did  not  understand.  But  I  have  the  consolation  that 
whole  nations  have  not  understood  it. 

Ingenuous  people  there  are  who  take  the  mock 
murders  of  the  stage  for  real  murders,  the  dissembled 
actions  of  the  players  for  real  actions,  and  who  can 
scarcely  restrain  themselves,  when  the  characters  of  the 
play  are  sorely  pressed,  from  running  in  deep  indigna- 
tion to  their  assistance.  Others,  again,  can  never  for- 
get that  the  beautiful  landscapes  of  the  stage  are 
painted,  that  Richard  III.  is  only  the  actor,  Mr. Booth, 
whom  they  have  met  time  and  again  at  the  clubs. 

Both  points  of  view  are  equally  mistaken.  To  look 
at  a  drama  or  a  picture  properly  one  must  understand 
that  both  are  shows,  simply  denoting  something  real. 
A  certain  preponderance  of  the  intellectual  life  over 
the  sensuous  life  is  requisite  for  such  an  achievement, 
where  the  intellectual  elements  are  safe  from  destruc- 
tion by  the  direct  sensuous  impressions.  A  certain 
liberty  in  choosing  one's  point  of  view  is  necessary,  a 
sort  of  humor,  I  might  say,  which  is  strongly  wanting 
in  children  and  in  childlike  peoples. 

Let  us  look  at  a  few  historical  facts.     I  shall  not 


78  WHY  HAS  MAN  TWO  EYES? 

take  you  as  far  back  as  the  stone  age,  although  we 
possess  sketches  from  this  epoch  which  show  very  orig- 
inal ideas  of  perspective.  But  let  us  begin  our  sight- 
seeing in  the  tombs  and  ruined  temples  of  ancient 
Egypt,  where  the  numberless  reliefs  and  gorgeous  col- 
orings have  defied  the  ravages  of  thousands  of  years. 

A  rich  and  motley  life  is  here  opened  to  us.  We 
find  the  Egyptians  represented  in  all  conditions  of  life. 
What  at  once  strikes  our  attention  in  these  pictures 
is  the  delicacy  of  their  technical  execution.  The  con- 
tours are  extremely  exact  and  distinct.  But  on  the 
other  hand  only  a  few  bright  colors  are  found,  un- 
blended and  without  trace  of  transition.  Shadows  are 
totally  wanting.  The  paint  is  laid  on  the  surfaces  in 
equal  thicknesses. 

Shocking  for  the  modern  eye  is  the  perspective. 
All  the  figures  are  equally  large,  with  the  exception  of 
the  king,  whose  form  is  unduly  exaggerated.  Near  and 
far  appear  equally  large.  Perspective  contraction  is 
nowhere  employed.  A  pond  with  water- fowl  is  repre- 
sented flat,  as  if  its  surface  were  vertical. 

Human  figures  are  portrayed  as  they  are  never 
seen,  the  legs  from  the  side,  the  face  in  profile.  The 
breast  lies  in  its  full  breadth  across  the  plane  of  rep- 
resentation. The  heads  of  cattle  appear  in  profile, 
while  the  horns  lie  in  the  plane  of  the  drawing.  The 
principle  which  the  Egyptians  followed  might  be  best 
expressed  by  saying  that  their  figures  are  pressed  in 


WHY  HAS  MAN  TWO  E  YES  ?  79 

the  plane  of  the  drawing  as  plants  are  pressed  in  a 
herbarium. 

The  matter  is  simply  explained.  If  the  Egyptians 
were  accustomed  to  looking  at  things  ingenuously 
with  both  eyes  at  once,  the  construction  of  perspec- 
tive pictures  in  space  could  not  be  familiar  to  them. 
They  saw  all  arms,  all  legs  on  real  men  in  their  nat- 
ural lengths.  The  figures  pressed  into  the  planes  re- 
sembled more  closely,  of  course,  in  their  eyes  the 
originals  than  perspective  pictures  could. 

This  will  be  better  understood  if  we  reflect  that 
painting  was  developed  from  relief.  The  minor  dis- 
similarities between  the  pressed  figures  and  the  orig- 
inals must  gradually  have  compelled  men  to  the  adop- 
tion of  perspective  drawing.  But  physiologically  the 
painting  of  the  Egyptions  is  just  as  much  justified  as 
the  drawings  of  our  children  are. 

A  slight  advance  beyond  the  Egyptians  is  shown 
by  the  Assyrians.  The  reliefs  rescued  from  the  ruined 
mounds  of  Nimrod  at  Mossul  are,  upon  the  whole, 
similar  to  the  Egyptian  reliefs.  They  were  made  known 
to  us  principally  by  Layard. 

Painting  enters  on  a  new  phase  among  the  Chi- 
nese. This  people  have  a  marked  feeling  for  perspec- 
tive and  correct  shading,  yet  without  being  very  logi- 
cal in  the  application  of  their  principles.  Here,  too, 
it  seems,  they  took  the  first  step  but  did  not  go  far. 
In  harmony  with  this  immobility  is  their  constitution, 
in  which  the  muzzle  and  the  bamboo-rod  play  sig- 


8o  WHY  HAS  MAN  7 WO  EYES? 

nificant  functions.  In  accord  with  it,  too,  is  their 
language,  which  like  the  language  of  children  has  not 
yet  developed  into  a  grammar,  or,  rather,  according 
to  the  modern  conception,  has  not  yet  degenerated 
into  a  grammar.  It  is  the  same  also  with  their  music 
which  is  satisfied  with  the  five-toned  scale. 

The  mural  paintings  at  Herculaneum  and  Pompeii 
are  distinguished  by  grace  of  representation,  as  also 
by  a  pronounced  sense  for  perspective  and  correct  il- 
lumination, yet  they  are  not  at  all  scrupulous  in  con- 
struction. Here  still  we  find  abbreviations  avoided. 
But  to  offset  this  defect,  the  members  of  the  body  are 
brought  into  unnatural  positions,  in  which  they  appear 
in  their  full  lengths.  Abridgements  are  more  fre- 
quently observed  in  clothed  than  in  unclothed  figures. 
A  satisfactory  explanation  of  these  phenomena  first 
occurred  to  me  on  the  making  of  a  few  simple  experi- 
ments which  show  how  differently  one  may  see  the 
same  object,  after  some  mastery  of  one's  senses  has 
been  attained,  simply  by  the  arbitrary 
movement  of  the  attention. 

Look  at  the  annexed  drawing  (Fig.  22). 
It  represents  a  folded  sheet  of  paper  with 
either  its  depressed  or  its  elevated  side 
turned  towards  you,  as  you  wish.  You  can 
conceive  the  drawing  in  either  sense,  and 
in  either  case  it  will  appear  to  you  differently. 

If,  now,  you  have  a  real  folded  sheet  of  paper  on 
the  table  before  you,  with  its  sharp  edges  turned  to- 


WHY  HAS  MAN  TWO  EYES?  81 

wards  you,  you  can,  on  looking  at  it  with  one  eye,  see 
the  sheet  alternately  elevated,  as  it  really  is,  or  de- 
pressed. Here,  however,  a  remarkable  phenomenon 
is  presented.  When  you  see  the  sheet  properly,  neither 
illumination  nor  form  presents  anything  conspicuous. 
When  you  see  it  bent  back  you  see  it  perspectively 
distorted.  Light  and  shadow  appear  much  brighter 
or  darker,  or  as  if  overlaid  thickly  with  bright  colors. 
Light  and  shadow  now  appear  devoid  of  all  cause. 
They  no  longer  harmonise  with  the  body's  form,  and 
are  thus  rendered  much  more  prominent. 

In  common  life  we  employ  the  perspective  and 
illumination  of  objects  to  determine  their  forms  and 
position.  Hence  we  do  not  notice  the  lights,  the 
shadows,  and  the  distortions.  They  first  powerfully 
enter  consciousness  when  we  employ  a  different  con- 
struction from  the  usual  spatial  one.  In  looking  at 
the  planar  image  of  a  camera  obscura  we  are  amazed 
at  the  plenitude  of  the  light  and  the  profundity  of  the 
shadows,  both  of  which  we  do  not  notice  in  real  ob- 
jects. 

In  my  earliest  youth  the  shadows  and  lights  on  pic- 
tures appeared  to  me  as  spots  void  of  meaning.  When 
I  began  to  draw  I  regarded  shading  as  a  mere  custom 
of  artists.  I  once  drew  the  portrait  of  our  pastor,  a 
friend  of  the  family,  and  shaded,  from  no  necessity, 
but  simply  from  having  seen  something  similar  in 
other  pictures,  the  whole  half  of  his  face  black.  I  was 
subjected  for  this  to  a  severe  criticism  on  the  part  of 


82  WHY  HAS  MAN  TWO  EYES? 

my  mother,  and  my  deeply  offended  artist's  pride  is 
probably  the  reason  that  these  facts  remained  so 
strongly  impressed  upon  my  memory. 

You  see,  then,  that  many  strange  things,  not  only 
in  the  life  of  individuals,  but  also  in  that  of  humanity, 
and  in  the  history  of  general  civilisation,  may  be  ex- 
plained from  the  simple  fact  that  man  has  two  eyes. 

Change  man's  eye  and  you  change  his  conception 
of  the  world.  We  have  observed  the  truth  of  this  fact 
among  our  nearest  kin,  the  Egyptians,  the  Chinese, 
and  the  lake- dwellers  ;  how  must  it  be  among  some  of 
our  remoter  relatives, — with  monkeys  and  other  ani- 
mals ?  Nature  must  appear  totally  different  to  animals 
equipped  with  substantially  different  eyes  from  those 
of  men,  as,  for  example,  to  insects.  But  for  the  pres- 
ent science  must  forego  the  pleasure  of  portraying  this 
appearance,  as  we  know  very  little  as  yet  of  the  mode 
of  operation  of  these  organs. 

It  is  an  enigma  even  how  nature  appears  to  ani- 
mals closely  related  to  man ;  as  to  birds,  who  see 
scarcely  anything  with  two  eyes  at  once,  but  since 
their  eyes  are  placed  on  opposite  sides  of  their  heads, 
have  a  separate  field  of  vision  for  each.* 

The  soul  of  man  is  pent  up  in  the  prison-house  of 
his  head ;  it  looks  at  nature  through  its  two  windows, 
the  eyes.  It  would  also  fain  know  how  nature  looks 
through  other  windows.  A  desire  apparently  never  to 

*  See  Job.  Mailer,  Vergleichende  Physiologic  dei  Gesichtstinnes,  Leipsic, 
1826. 


WHY  HAS  MAN  TWO  E  YES  ?  83 

be  fulfilled.  But  our  love  for  nature  is  inventive,  and 
here,  too,  much  has  been  accomplished. 

Placing  before  me  an  angular  mirror,  consisting  of 
two  plane  mirrors  slightly  inclined  to  each  other,  I  see 
my  face  twice  reflected.  In  the  right-hand  mirror  I 
obtain  a  view  of  the  right  side,  and  in  the  left-hand 
mirror  a  view  of  the  left 
side,  of  my  face.  Also 
I  shall  see  the  face  of  a 

Fig.  23. 

person  standing  in  front 

of  me,  more  to  the  right  with  my  right  eye,  more  to 
the  left  with  my  left.  But  in  order  to  obtain  such 
widely  different  views  of  a  face  as  those  shown  in  the 
angular  mirror,  my  two  eyes  would  have  to  be  set  much 
further  apart  from  each  other  than  they  actually  are. 

Squinting  with  my  right  eye  at  the  image  in  the 
right-hand  mirror,  with  my  left  eye  at  the  image  in 
the  left-hand  mirror,  my  vision  will  be  the  vision  of  a 
giant  having  an  enormous  head  with  his  two  eyes  set 
far  apart.  This,  also,  is  the  impression  which  my  own 
face  makes  upon  me.  I  see  it  now,  single  and  solid. 
Fixing  my  gaze,  the  relief  from  second  to  second  is 
magnified,  the  eyebrows  start  forth  prominently  from 
above  the  eyes,  the  nose  seems  to  grow  a  foot  in 
length,  my  mustache  shoots  forth  like  a  fountain  from 
my  lip,  the  teeth  seem  to  retreat  immeasurably.  But 
by  far  the  most  horrible  aspect  of  the  phenomenon  is 
the  nose. 

Interesting  in  this  connexion  is  the  telestereoscope 


.    \ 
T^ 


84  WHY  HAS  MAN  TWO  EYES? 

of  Helmholtz.  In  the  telestereoscope  we  view  a  land- 
scape by  looking  with  our  right  eye  (Fig.  24)  through 
the  mirror  a  into  the  mirror  A,  and  with  our  left  eye 
through  the  mirror  b  into  the  mirror  B.  The  mirrors 
A  and  .Z?  stand  far  apart.  •  i 

Again  we  see  with  the 
widely  separated  eyes 
of  a  giant.  Everything 
appears  dwarfed  and 
near  us.  The  distant  Fig.  24. 

mountains     look     like 

moss-covered  stones  at  our  feet.  Between,  you  see  the 
reduced  model  of  a  city,  a  veritable  Liliput.  You 
are  tempted  almost  to  stroke  with  your  hand  the  soft 
forest  and  city,  did  you  not  fear  that  you  might  prick 
your  fingers  on  the  sharp,  needle-shaped  steeples,  or 
that  they  might  crackle  and  break  off. 

Liliput  is  no  fable.  We  need  only  Swift's  eyes, 
the  telestereoscope,  to  see  it. 

Picture  to  yourself  the  reverse  case.  Let  us  sup- 
pose ourselves  so  small  that  we  could  take  long  walks 
in  a  forest  of  moss,  and  that  our  eyes  were  correspond- 
ingly near  each  other.  The  moss-fibres  would  appear 
like  trees.  On  them  we  should  see  strange,  unshapely 
monsters  creeping  about.  Branches  of  the  oak-tree, 
at  whose  base  our  moss-forest  lay,  would  seem  to  us 
dark,  immovable,  myriad-branched  clouds,  painted 
high  on  the  vault  of  heaven  ;  just  as  the  inhabitants 
of  Saturn,  forsooth,  might  see  their  enormous  ring. 


WHY  HAS  MAN  TWO  EYES  t  85 

On  the  tree-trunks  of  our  mossy  woodland  we  should 
find  colossal  globes  several  feet  in  diameter,  brilliantly 
transparent,  swayed  by  the  winds  with  slow,  peculiar 
motions.  We  should  approach  inquisitively  and  should 
find  that  these  globes,  in  which  here  and  there  ani- 
mals were  gaily  sporting,  were  liquid  globes,  in  fact 
that  they  were  water.  A  short,  incautious  step,  the 
slightest  contact,  and  woe  betide  us,  our  arm  is  irresist- 
ibly drawn  by  an  invisible  power  into  the  interior  of 
the  sphere  and  held  there  unrelentingly  fast !  A  drop 
of  dew  has  engulfed  in  its  capillary  maw  a  manikin, 
in  revenge  for  the  thousands  of  drops  that  its  big  hu- 
man counterparts  have  quaffed  at  breakfast.  Thou 
shouldst  have  known,  thou  pygmy  natural  scientist, 
that  with  thy  present  puny  bulk  thou  shouldst  not  joke 
with  capillarity ! 

My  terror  at  the  accident  brings  me  back  to  my 
senses.  I  see  I  have  turned  idyllic.  You  must  pardon 
me.  A  patch  of  greensward,  a  moss  or  heather  forest 
with  its  tiny  inhabitants  have  incomparably  more 
charms  for  me  than  many  a  bit  of  literature  with  its 
apotheosis  of  human  character.  If  I  had  the  gift  of 
writing  novels  I  should  certainly  not  make  John  and 
Mary  my  characters.  Nor  should  I  transfer  my  loving 
pair  to  the  Nile,  nor  to  the  age  of  the  old  Egyptian 
Pharaohs,  although  perhaps  I  should  choose  that  time 
in  preference  to  the  present.  For  I  must  candidly 
confess  that  I  hate  the  rubbish  of  history,  interesting 
though  it  may  be  as  a  mere  phenomenon,  because  we 


86  WHY  HAS  MAN  TWO  EYES? 

cannot  simply  observe  it  but  must  also/<r^/  it,  because 
it  comes  to  us  mostly  with  supercilious  arrogance, 
mostly  unvanquished.  The  hero  of  my  novel  would  be 
a  cockchafer,  venturing  forth  in  his  fifth  year  for  the 
first  time  with  his  newly  grown  wings  into  the  light, 
free  air.  Truly  it  could  do  no  harm  if  man  would  thus 
throw  off  his  inherited  and  acquired  narrowness  of 
mind  by  making  himself  acquainted  with  the  world- 
view  of  allied  creatures.  He  could  not  help  gaining 
incomparably  more  in  this  way  than  the  inhabitant  of 
a  small  town  would  in  circumnavigating  the  globe  and 
getting  acquainted  with  the  views  of  strange  peoples. 

* 
*  * 

I  have  now  conducted  you,  by  many  paths  and  by- 
ways, rapidly  over  hedge  and  ditch,  to  show  you  what 
wide  vistas  we  may  reach  in  every  field  by  the  rigor- 
ous pursuit  of  a  single  scientific  fact.  A  close  exam- 
ination of  the  two  eyes  of  man  has  conducted  us  not 
only  into  the  dim  recesses  of  humanity's  childhood, 
but  has  also  carried  us  far  beyond  the  bourne  of  human 
life. 

It  has  surely  often  struck  you  as  strange  that  the 
sciences  are  divided  into  two  great  groups ;  that  the 
so-called  humanistic  sciences,  belonging  to  the  so- 
called  "higher  education,"  are  placed  in  almost  a  hos- 
tile attitude  to  the  natural  sciences. 

I  must  confess  I  do  not  overmuch  believe  in  this 
partition  of  the  sciences.  I  believe  that  this  view  will 
appear  as  childlike  and  ingenuous  to  a  matured  age 


WHY  HAS  MAN  TWO  E  YES  ?  87 

as  the  want  of  perspective  in  the  old  paintings  of  Egypt 
does  to  us.  Can  it  really  be  that  "higher  culture"  is  to 
be  gotten  only  from  a  few  old  pots  and  palimpsests, 
which  are  at  best  mere  scraps  of  nature,  or  that  more 
is  to  be  learned  from  them  alone  than  from  all  the  rest 
of  nature  ?  I  believe  that  both  these  sciences  are  sim- 
ply parts  of  the  same  science,  which  have  begun  at 
different  ends.  If  these  two  ends  still  act  towards 
each  other  as  the  Montagues  and  Capulets,  if  their  re- 
tainers still  indulge  in  lively  tilts,  I  believe  that  after 
all  they  are  not  in  earnest.  On  the  one  side  there  is 
surely  a  Romeo,  and  on  the  other  a  Juliet,  who,  some 
day,  it  is  hoped,  will  unite  the  two  houses  with  a  less 
tragic  sequel  than  that  of  the  play. 

Philology  began  with  the  unqualified  reverence  and 
apotheosis  of  the  Greeks.  Now  it  has  begun  to  draw 
other  languages,  other  peoples  and  their  histories,  into 
its  sphere  ;  it  has,  through  the  mediation  of  compara- 
tive linguistics,  already  struck  up,  though  as  yet  some- 
what cautiously,  a  friendship  with  physiology. 

Physical  science  began  in  the  witch's  kitchen.  It 
now  embraces  the  organic  and  inorganic  worlds,  and 
with  the  physiology  of  articulation  and  the  theory  of 
the  senses,  has  even  pushed  its  researches,  at  times 
impertinently,  into  the  province  of  mental  phenomena. 

In  short,  we  come  to  the  understanding  of  much 
within  us  solely  by  directing  our  glance  without,  and 
vice  versa.  Every  object  belongs  to  both  sciences. 
You,  ladies,  are  very  interesting  and  difficult  problems 


88  WHY  HAS  MAN  TWO  EYES  ? 

for  the  psychologist,  but  you  are  also  extremely  pretty 
phenomena  of  nature.  Church  and  State  are  objects 
of  the  historian's  research,  but  not  less  phenomena  of 
nature,  and  in  part,  indeed,  very  curious  phenomena. 
If  the  historical  sciences  have  inaugurated  wide  ex- 
tensions of  view  by  presenting  to  us  the  thoughts  of 
new  and  strange  peoples,  the  physical  sciences  in  a 
certain  sense  do  this  in  a  still  greater  degree.  In 
making  man  disappear  in  the  All,  in  annihilating  him, 
so  to  speak,  they  force  him  to  take  an  unprejudiced 
position  without  himself,  and  to  form  his  judgments  by 
a  different  standard  from  that  of  the  petty  human. 

But  if  you  should  ask  me  now  why  man  has  two 
eyes,  I  should  answer  : 

That  he  may  look  at  nature  justly  and  accurately; 
that  he  may  come  to  understand  that  he  himself,  with 
all  his  views,  correct  and  incorrect,  with  all  his  haute 
politique,  is  simply  an  evanescent  shred  of  nature ; 
that,  to  speak  with  Mephistopheles,  he  is  a  part  of  the 
part,  and  that  it  is  absolutely  unjustified, 

11  For  man,  the  microcosmic  fool,  to  see 
Himself  a  whole  so  frequently." 


ON  SYMMETRY.' 


AN  ancient  philosopher  once  remarked  that  people 
•*%  who  cudgelled  their  brains  about  the  nature  of 
the  moon  reminded  him  of  men  who  discussed  the 
laws  and  institutions  of  a  distant  city  of  which  they 
had  heard  no  more  than  the  name.  The  true  philoso- 
pher, he  said,  should  turn  his  glance  within,  should 
study  himself  and  his  notions  of  right  and  wrong  ;  only 
thence  could  he  derive  real  profit. 

This  ancient  formula  for  happiness  might  be  re- 
stated in  the  familiar  words  of  the  Psalm  : 

"Dwell  in  the  land,  and  verily  thou  shalt  be  fed." 

To-day,  if  he  could  rise  from  the  dead  and  walk 
about  among  us,  this  philosopher  would  marvel  much 
at  the  different  turn  which  matters  have  taken. 

'Delivered  before  the  German  Casino  of  Prague,  in  the  winter  of  1871. 

A  fuller  treatment  of  the  problems  of  this  lecture  will  be  found  in  my  Con- 
tributions to  the  Analysis  of  the  Sensations  (Jena,  1886),  English  Translation, 
Chicago,  1895.  J.  P.  Soret,  Sur  la  perception  du  beau  (Geneva,  1892),  also  re- 
gards repetition  as  a  principle  of  aesthetics.  His  discussions  of  the  eesthetical 
side  of  the  subject  are  much  more  detailed  than  mine.  But  with  respect  to 
the  psychological  and  physiological  foundation  of  the  principle,  I  am  con- 
vinced that  the  Contributions  to  the  Analysis  of  the  Sensations  go  deeper. — 
MACH  (1894). 


go  ON  SYMMETRY. 

The  motions  of  the  moon  and  the  other  heavenly 
bodies  are  accurately  known.  Our  knowledge  of  the 
motions  of  our  own  body  is  by  far  not  so  complete. 
The  mountains  and  natural  divisions  of  the  moon  have 
been  accurately  outlined  on  maps,  but  physiologists 
are  just  beginning  to  find  their  way  in  the  geography 
of  the  brain.  The  chemical  constitution  of  many  fixed 
stars  has  already  been  investigated.  The  chemical 
processes  of  the  animal  body  are  questions  of  much 
greater  difficulty  and  complexity.  We  have  our  Me- 
canique  celeste.  But  a  Mecanique  so  dale  or  a  Mecanique 
morale  of  equal  trustworthiness  remains  to  be  written. 

Our  philosopher  would  indeed  admit  that  we  have 
made  great  progress.  But  we  have  not  followed  his 
advice.  The  patient  has  recovered,  but  he  took  for  his 
recovery  exactly  the  opposite  of  what  the  doctor  pre- 
scribed. 

Humanity  is  now  returned,  much  wiser,  from  its 
journey  in  celestial  space,  against  which  it  was  so 
solemnly  warned.  Men,  after  having  become  acquainted 
with  the  great  and  simple  facts  of  the  world  without, 
are  now  beginning  to  examine  critically  the  world 
within.  It  sounds  absurd,  but  it  is  true,  that  only  after 
we  have  thought  about  the  moon  are  we  able  to  take 
up  ourselves.  It  was  necessary  that  we  should  acquire 
simple  and  clear  ideas  in  a  less  complicated  domain, 
before  we  entered  the  more  intricate  one  of  psychol- 
ogy, and  with  these  ideas  astronomy  principally  fur- 
nished us. 


ON  SYMMETRY.  91 

To  attempt  any  description  of  that  stupendous 
movement,  which,  originally  springing  out  of  the  phys- 
ical sciences,  went  beyond  the  domain  of  physics  and  is 
now  occupied  with  the  problems  of  psychology,  would 
be  presumptuous  in  this  place.  I  shall  only  attempt 
here,  to  illustrate  to  you  by  a  few  simple  examples  the 
methods  by  which  the  province  of  psychology  can  be 
reached  from  the  facts  of  the  physical  world — especially 
the  adjacent  province  of  sense-perception.  And  I  wish 
it  to  be  remembered  that  my  brief  attempt  is  not  to  be 
taken  as  a  measure  of  the  present  state  of  such  scien- 
tific questions. 

*         *         * 

It  is  a  well-known  fact  that  some  objects  please  us, 
while  others  do  not.  Generally  speaking,  anything 
that  is  constructed  according  to  fixed  and  logically 
followed  rules,  is  a  product  of  tolerable  beauty.  We  see 
thus  nature  herself,  who  always  acts  according  to  fixed 
rules,  constantly  producing  such  pretty  things.  Every 
day  the  physicist  is  confronted  in  his  workshop  with 
the  most  beautiful  vibration-figures,  tone-figures,  phe- 
nomena of  polarisation,  and  forms  of  diffraction. 

A  rule  always  presupposes  a  repetition.  Repeti- 
tions, therefore,  will  probably  be  found  to  play  some 
important  part  in  the  production  of  agreeable  effects. 
Of  course,  the  nature  of  agreeable  effects  is  not  ex- 
hausted by  this.  Furthermore,  the  repetition  of  a 
physical  event  becomes  the  source  of  agreeable  effects 


92  ON  SYMMETRY. 

only  when  it  is  connected  with  a  repetition  of  sensa- 
tions. 

An  excellent  example  that  repetition  of  sensations 
is  a  source  of  agreeable  effects  is  furnished  by  the 
copy-book  of  every  schoolboy,  which  is  usually  a  treas- 
ure-house of  such  things,  and  only  in  need  of  an  Abb6 
Domenech  to  become  celebrated.  Any  figure,  no  mat- 
ter how  crude  or  poor,  if  several  times  repeated,  with 
the  repetitions  placed  in  line,  will  produce  a  tolerable 
frieze. 


Fig.  25. 

Also  the  pleasant  effect  of  symmetry  is  due  to  the 
repetition  of  sensations.  Let  us  abandon  ourselves  a 
moment  to  this  thought,  yet  not  imagine  when  we  have 
developed  it,  that  we  have  fully  exhausted  the  nature 
of  the  agreeable,  much  less  of  the  beautiful. 

First,  let  us  get  a  clear  conception  of  what  sym- 
metry is.  And  in  preference  to  a  definition  let  us  take 
a  living  picture.  You  know  that  the  reflexion  of  an 
object  in  a  mirror  has  a  great  likeness  to  the  object  it- 
self. All  its  proportions  and  outlines  are  the  same. 


ON  SYMMETRY.  93 

Yet  there  is  a  difference  between  the  object  and  its  re- 
flexion in  the  mirror,  which  you  will  readily  observe. 

Hold  your  right  hand  before  a  mirror,  and  you  will 
see  in  the  mirror  a  left  hand.  Your  right  glove  will 
produce  its  mate  in  the  glass.  For  you  could  never 
use  the  reflexion  of  your  right  glove,  if  it  were  present 
to  you  as  a  real  thing,  for  covering  your  right  hand, 
but  only  for  covering  your  left.  Similarly,  your  right 
ear  will  give  as  its  reflexion  a  left  ear  ;  and  you  will  at 
once  perceive  that  the  left  half  of  your  body  could  very 
easily  be  substituted  for  the  reflexion  of  your  right  half. 
Now  just  as  in  the  place  of  a  missing  right  ear  a  left  ear 
cannot  be  put,  unless  the  lobule  of  the  ear  be  turned  up- 
wards, or  the  opening  into  the  concha  backwards,  so, 
despite  all  similarity  of  form,  the  reflexion  of  an  ob- 
ject can  never  take  the  place  of  the  object  itself.* 

The  reason  of  this  difference  between  the  object 
and  its  reflexion  is  simple.  The  reflexion  appears  as 
far  behind  the  mirror  as  the  object  is  in  front  of  it.  The 
parts  of  the  object,  accordingly,  which  are  nearest  the 
mirror  will  also  be  nearest  the  mirror  in  the  reflexion. 
Consequently,  the  succession  of  the  parts  in  the  re- 
flexion will  be  reversed,  as  may  best  be  seen  in  the  re- 
flexion of  the  face  of  a  watch  or  of  a  manuscript. 

It  will  also  be  readily  seen,  that  if  a  point  of  the  ob- 
ject be  joined  with  its  reflexion  in  the  image,  the  line 
of  junction  will  cut  the  mirror  at  right  angles  and  be 


*  Kant,  in  his  Prolegomena  zu  jtdtr  kUnfligen  Metaphysik,  also  refers  to 
this  fact,  but  for  a  different  purpose. 


94  ON  S  YMME  TR  Y. 

bisected  by  it.     This  holds  true  of  all  corresponding 
points  of  object  and  image. 

If,  now,  we  can  divide  an  object  by  a  plane  into 
two  halves  so  that  each  half,  as  seen  in  the  reflecting 
plane  of  division,  is  a  reproduction  of  the  other  half, 
such  an  object  is  termed  symmetrical,  and  the  plane 
of  division  is  called  the  plane  of  symmetry. 

If  the  plane  of  symmetry  is  vertical,  we  can  say 
that  the  body  is  vertically  symmetrical.  An  example 
of  vertical  symmetry  is  a  Gothic  cathedral. 

If  the  plane  of  symmetry  is  horizontal,  we  can  say 
that  the  object  is  horizontally  symmetrical.  A  land- 
scape on  the  shores  of  a  lake  with  its  reflexion  in  the 
water,  is  a  system  of  horizontal  symmetry. 

Exactly  here  is  a  noticeable  difference.  The  ver- 
tical symmetry  of  a  Gothic  cathedral  strikes  us  at  once, 
whereas  we  can  travel  up  and  down  the  whole  length 
of  the  Rhine  or  the  Hudson  without  becoming  aware 
of  the  symmetry  between  objects  and  their  reflexions 
in  the  water.  Vertical  symmetry  pleases  us,  whilst 
horizontal  symmetry  is  indifferent,  and  is  noticed  only 
by  the  experienced  eye. 

Whence  arises  this  difference  ?  I  say  from  the  fact 
that  vertical  symmetry  produces  a  repetition  of  the 
same  sensation,  while  horizontal  symmetry  does  not. 
I  shall  now  show  that  this  is  so. 

Let  us  look  at  the  following  letters  : 
d     b 

q   p 


ON  SYMMETRY.  95 

It  is  a  fact  known  to  all  mothers  and  teachers,  that 
children  in  their  first  attempts  to  read  and  write,  con- 
stantly confound  d  and  b,  and  q  and  p,  but  never  d 
and  q,  or  b  and  p.  Now  d  and  b  and  q  and  p  are  the 
two  halves  of  a  vertically  symmetrical  figure,  while  d 
and  q,  and  b  and  p  are  two  halves  of  a  horizontally  sym- 
metrical figure.  The  first  two  are  confounded ;  but 
confusion  is  only  possible  of  things  that  excite  in  us 
the  same  or  similar  sensations. 

Figures  of  two  flower-girls  are  frequently  seen  on 
the  decorations  of  gardens  and  of  drawing-rooms,  one 
of  whom  carries  a  flower-basket  in  her  right  hand  and 
the  other  a  flower-basket  in  her  left.  All  know  how 
apt  we  are,  unless  we  are  very  careful,  to  confound  these 
figures  with  one  another. 

While  turning  a  thing  round  from  right  to  left  is 
scarcely  noticed,  the  eye  is  not  at  all  indifferent  to  the 
turning  of  a  thing  upside  down.  A  human  face  which 
has  been  turned  upside  down  is  scarcely  recognisable 
as  a  face,  and  makes  an  impression  which  is  altogether 
strange.  The  reason  of  this  is  not  to  be  sought  in  the 
unwontedness  of  the  sight,  for  it  is  just  as  difficult  to 
recognise  an  arabesque  that  has  been  inverted,  where 
there  can  be  no  question  of  a  habit.  This  curious  fact 
is  the  foundation  of  the  familiar  jokes  played  with  the 
portraits  of  unpopular  personages,  which  are  so  drawn 
that  in  the  upright  position  of  the  page  an  exact  pic- 
ture of  the  person  is  presented,  but  on  being  inverted 
some  popular  animal  is  shown. 


g6  ON  SYMMETRY. 

It  is  a  fact,  then,  that  the  two  halves  of  a  vertically 
symmetrical  figure  are  easily  confounded  and  that  they 
therefore  probably  produce  very  nearly  the  same  sen- 
sations. The  question,  accordingly,  arises,  why  do  the 
two  halves  of  a  vertically  symmetrical  figure  produce 
the  same  or  similar  sensations?  The  answer  is  :  Be- 
cause our  apparatus  of  vision,  which  consists  of  our 
eyes  and  of  the  accompanying  muscular  apparatus  is 
itself  vertically  symmetrical.* 

Whatever  external  resemblances  one  eye  may  have 
with  another  they  are  still  not  alike.  The  right  eye  of 
a  man  cannot  take  the  place  of  a  left  eye  any  more 
than  a  left  ear  or  left  hand  can  take  the  place  of  a 
right  one.  By  artificial  means,  we  can  change  the  part 
which  each  of  our  eyes  plays.  (Wheatstone's  pseudo- 
scope.)  But  we  then  find  ourselves  in  an  entirely  new 
and  strange  world.  What  is  convex  appears  concave  ; 
what  is  concave,  convex.  What  is  distant  appears 
near,  and  what  is  near  appears  far. 

The  left  eye  is  the  reflexion  of  the  right.  And  the 
light-feeling  retina  of  the  left  eye  is  a  reflexion  of  the 
light-feeling  retina  of  the  right,  in  all  its  functions. 

The  lense  of  the  eye,  like  a  magic  lantern,  casts 
images  of  objects  on  the  retina.  And  you  may  picture 
to  yourself  the  light-feeling  retina  of  the  eye,  with  its 
countless  nerves,  as  a  hand  with  innumerable  fingers, 
adapted  to  feeling  light.  The  ends  of  the  visual  nerves, 
like  our  fingers,  are  endowed  with  varying  degrees  of 

*  Compare  Mach,  Fichte's  Zeitschriftfiir  Philosophie,  1864,  p.  I. 


ON  SYMMETRY.  97 

sensitiveness.  The  two  retinae  act  like  a  right  and  a 
left  hand  ;  the  sensation  of  touch  and  the  sensation  of 
light  in  the  two  instances  are  similar. 

Examine  the  right-hand  portion  of  this  letter  T  : 
namely,  T.  Instead  of  the  two  retinae  on  which  this 
image  falls,  imagine  feeling  the  object,  my  two  hands. 
The  F,  grasped  with  the  right  hand,  gives  a  different 
sensation  from  that  which  it  gives  when  grasped  with 
the  left.  But  if  we  turn  our  character  about  from  right 
to  left,  thus  :  1 ,  it  will  give  the  same  sensation  in  the 
left  hand  that  it  gave  before  in  the  right.  The  sensa- 
tion is  repeated. 

If  we  take  a  whole  T,  the  right  half  will  produce  in 
the  right  hand  the  same  sensation  that  the  left  half 
produces  in  the  left,  and  vice  versa. 

The  symmetrical  figure  gives  the  same  sensation 
twice. 

If  we  turn  the  T  over  thus  :  H  >  or  invert  the  half 
T  thus  :  L,  so  long  as  we  do  not  change  the  position 
of  our  hands  we  can  make  no  use  of  the  foregoing  rea- 
soning. 

The  retinae,  in  fact,  are  exactly  like  our  two  hands. 
They,  too,  have  their  thumbs  and  index  fingers,  though 
they  are  thousands  in  number;  and  we  may  say  the 
thumbs  are  on  the  side  of  the  eye  near  the  nose, 
and  the  remaining  fingers  on  the  side  away  from  the 
nose. 

With  this  I  hope  to  have  made  perfectly  clear  that 
the  pleasing  effect  of  symmetry  is  chiefly  due  to  the 


98  ON  SYMMETRY. 

repetition  of  sensations,  and  that  the  effect  in  ques- 
tion takes  place  in  symmetrical  figures,  only  where 
there  is  a  repetition  of  sensation.  The  pleasing  effect 
of  regular  figures,  the  preference  which  straight  lines, 
especially  vertical  and  horizontal  straight  lines,  en- 
joy, is  founded  on  a  similar  reason.  A  straight  line, 
both  in  a  horizontal  and  in  a  vertical  position,  can  cast 
on  the  two  retinae  the  same  image,  which  falls  more- 
over on  symmetrically  corresponding  spots.  This  also, 
it  would  appear,  is  the  reason  of  our  psychological 
preference  of  straight  to  curved  lines,  and  not  their 
property  of  being  the  shortest  distance  between  two 
points.  The  straight  line  is  felt,  to  put  the  matter 
briefly,  as  symmetrical  to  itself,  which  is  the  case  also 
with  the  plane.  Curved  lines  are  felt  as  deviations 
from  straight  lines,  that  is,  as  deviations  from  symme- 
try.* The  presence  of  a  sense  for  symmetry  in  people 
possessing  only  one  eye  from  birth,  is  indeed  a  riddle. 
Of  course,  the  sense  of  symmetry,  although  primarily 
acquired  by  means  of  the  eyes,  cannot  be  wholly  lim- 
ited to  the  visual  organs.  It  must  also  be  deeply 
rooted  in  other  parts  of  the  organism  by  ages  of  prac- 
tice and  can  thus  not  be  eliminated  forthwith  by  the 
loss  of  one  eye.  Also,  when  an  eye  is  lost,  the  sym- 


*The  fact  that  the  first  and  second  differential  coefficients  of  a  curve  are 
directly  seen,  but  the  higher  coefficients  not,  is  very  simply  explained.  The 
first  gives  the  position  of  the  tangent,  the  declination  of  the  straight  line  from 
the  position  of  symmetry,  the  second  the  declination  of  the  curve  from  the 
straight  line.  It  is,  perhaps,  not  unprofitable  to  remark  here  that  the  ordi- 
nary method  of  testing  rulers  and  plane  surfaces  (by  reversed  applications) 
ascertains  the  deviation  of  the  object  from  symmetry  to  itself. 


ON  SYMMETRY.  99 

metrical  muscular  apparatus  is  left,  as  is  also  the 
symmetrical  apparatus  of  innervation. 

It  appears,  however,  unquestionable  that  the  phe- 
nomena mentioned  have,  in  the  main,  their  origin  in 
the  peculiar  structure  of  our  eyes.  It  will  therefore 
be  seen  at  once  that  our  notions  of  what  is  beautiful 
and  ugly  would  undergo  a  change  if  our  eyes  were  dif- 
ferent. Also,  if  this  view  is  correct,  the  theory  of  the 
so-called  eternally  beautiful  is  somewhat  mistaken.  It 
can  scarcely  be  doubted  that  our  culture,  or  form  of 
civilisation,  which  stamps  upon  the  human  body  its 
unmistakable  traces,  should  not  also  modify  our  con- 
ceptions of  the  beautiful.  Was  not  formerly  the  de- 
velopment of  all  musical  beauty  restricted  to  the  nar- 
row limits  of  a  five-toned  scale  ? 

The  fact  that  a  repetition  of  sensations  is  produc- 
tive of  pleasant  effects  is  not  restricted  to  the  realm  of 
the  visible.  To-day,  both  the  musician  and  the  phys- 
icist know  that  the  harmonic  or  the  melodic  addition 
of  one  tone  to  another  affects  us  agreeably  only  when 
the  added  tone  reproduces  a  part  of  the  sensation 
which  the  first  one  excited.  When  I  add  an  octave 
to  a  fundamental  tone,  I  hear  in  the  octave  a  part  of 
what  was  heard  in  the  fundamental  tone.  (Helm- 
holtz.)  But  it  is  not  my  purpose  to  develop  this  idea 
fully  here.*  We  shall  only  ask  to-day,  whether  there 
is  anything  similar  to  the  symmetry  of  figures  in  the 
province  of  sounds. 

•See  the  lecture  On  the  Causes  of  Harmony. 


ioo  ON  SYMMETRY. 

Look  at  the  reflexion  of  your  piano  in  the  mirror. 

You  will  at  once  remark  that  you  have  never  seen 
such  a  piano  in  the  actual  world,  for  it  has  its  high 
keys  to  the  left  and  its  low  ones  to  the  right.  Such 
pianos  are  not  manufactured. 

If  you  could  sit  down  at  such  a  piano  and  play  in 
your  usual  manner,  plainly  every  step  which  you 
imagined  you  were  performing  in  the  upward  scale 
would  be  executed  as  a  corresponding  step  in  the 
downward  scale.  The  effect  would  be  not  a  little  sur- 
prising. 

For  the  practised  musician  who  is  always  accus- 
tomed to  hearing  certain  sounds  produced  when  cer- 
tain keys  are  struck,  it  is  quite  an  anomalous  spectacle 
to  watch  a  player  in  the  glass  and  to  observe  that  he 
always  does  the  opposite  of  what  we  hear. 

But  still  more  remarkable  would  be  the  effect  of 
attempting  to  strike  a  harmony  on  such  a  piano.  For 
a  melody  it  is  not  indifferent  whether  we  execute  a 
step  in  an  upward  or  a  downward  scale.  But  for  a 
harmony,  so  great  a  difference  is  not  produced  by  re- 
versal. I  always  retain  the  same  consonance  whether 
I  add  to  a  fundamental  note  an  upper  or  a  lower  third. 
Only  the  order  of  the  intervals  of  the  harmony  is  re- 
versed. In  point  of  fact,  when  we  execute  a  move- 
ment in  a  major  key  on  our  reflected  piano,  we  hear  a 
sound  in  a  minor  key,  and  vice  versa. 

It  now  remains  to  execute  the  experiments  indi- 
cated. Instead  of  playing  upon  the  piano  in  the  mir- 


ON  SYMMETRY.  101 

ror,  which  is  impossible,  or  of  having  a  piano  of  this 
kind  built,  which  would  be  somewhat  expensive,  we 
may  perform  our  experiments  in  a  simpler  manner,  as 
follows : 

1)  We  play  on  our  own  piano  in  our  usual  manner, 
look  into  the  mirror,  and  then  repeat  on  our  real  piano 
what  we  see  in  the  mirror.     In  this  way  we  transform 
all  steps  upwards  into  corresponding  steps  downwards. 
We  play  a  movement,  and  then  another  movement, 
which,  with  respect  to  the  key-board,  is  symmetrical 
to  the  first. 

2)  We  place  a  mirror  beneath  the  music  in  which 
the  notes  are  reflected  as  in  a  body  of  water,  and  play 
according  to  the  notes  in  the  mirror.  In  this  way  also, 
all  steps  upwards  are  changed  into  corresponding, 
equal  steps  downwards. 

3)  We  turn  the  music  upside  down  and  read  the 
notes  from  right  to  left  and  from  below  upwards.     In 
doing  this,  we  must  regard  all  sharps  as  flats  and  all 
flats  as  sharps,  because  they  correspond  to  half  lines 
and  spaces.     Besides,  in  this  use  of  the  music  we  can 
only  employ  the  bass  clef,  as  only  in  this  clef  are  the 
notes  not  changed  by  symmetrical  reversal. 

You  can  judge  of  the  effect  of  these  experiments 
from  the  examples  which  appear  in  the  annexed  musi- 
cal cut.  (Page  102.)  The  movement  which  appears  in 
the  upper  lines  is  symmetrically  reversed  in  the  lower. 

The  effect  of  the  experiments  may  be  briefly  formu- 
lated. The  melody  is  rendered  unrecognisable.  The 


-f-ff^ 


Fig.  26. 
(See  pages  101  and  103.) 


ON  SYMMETRY.  103 

harmony  suffers  a  transposition  from  a  major  into  a 
minor  key  and  vice  versa.  The  study  of  these  pretty 
effects,  which  have  long  been  familiar  to  physicists 
and  musicians,  was  revived  some  years  ago  by  Von 
Oettingen.* 

Now,  although  in  all  the  preceding  examples  I  have 
transposed  steps  upward  into  equal  and  similar  steps 
downward,  that  is,  as  we  may  justly  say,  have  played 
for  every  movement  the  movement  which  is  symmetri- 
cal to  it,  yet  the  ear  notices  either  little  or  nothing  of 
symmetry.  The  transposition  from  a  major  to  a  minor 
key  is  the  sole  indication  of  symmetry  remaining.  The 
symmetry  is  there  for  the  mind,  but  is  wanting  for 
sensation.  No  symmetry  exists  for  the  ear,  because  a 
reversal  of  musical  sounds  conditions  no  repetition  of 
sensations.  If  we  had  an  ear  for  height  and  an  ear 
for  depth,  just  as  we  have  an  eye  for  the  right  and  an 
eye  for  the  left,  we  should  also  find  that  symmetrical 
sound- structures  existed  for  our  auditory  organs.  The 
contrast  of  major  and  minor  for  the  ear  corresponds  to 
inversion  for  the  eye,  which  is  also  only  symmetry  for 
the  mind,  but  not  for  sensation. 

By  way  of  supplement  to  what  I  have  said,  I  will 
add  a  brief  remark  for  my  mathematical  readers. 

Our  musical  notation  is  essentially  a  graphical  rep- 
resentation of  a  piece  of  music  in  the  form  of  curves, 
where  the  time  is  the  abscissae,  and  the  logarithms  of 


*  A.  von  Oettingen,  Harmoniesystem  in  dualer  Entwicklnng.     Leipsic  and 
Dorpat,  1866. 


104  ON  SYMMETRY. 

the  number  of  vibrations  the  ordinates.  The  devia- 
tions of  musical  notation  from  this  principle  are  only 
such  as  facilitate  interpretation,  or  are  due  to  histori- 
cal accidents. 

If,  now,  it  be  further  observed  that  the  sensation 
of  pitch  also  is  proportional  to  the  logarithm  of  the 
number  of  vibrations,  and  that  the  intervals  between 
the  notes  correspond  to  the  differences  of  the  loga- 
rithms of  the  numbers  of  vibrations,  the  justification 
will  be  found  in  these  facts  of  calling  the  harmonies 
and  melodies  which  appear  in  the  mirror,  symmetrical 

to  the  original  ones. 

* 
*  * 

I  simply  wish  to  bring  home  to  your  minds  by  these 
fragmentary  remarks  that  the  progress  of  the  physical 
sciences  has  been  of  great  help  to  those  branches  of 
psychology  that  have  not  scorned  to  consider  the  re- 
sults of  physical  research.  On  the  other  hand,  psy- 
chology is  beginning  to  return,  as  it  were,  in  a  spirit 
of  thankfulness,  the  powerful  stimulus  which  it  received 
from  physics. 

The  theories  of  physics  which  reduce  all  phenom- 
ena to  the  motion  and  equilibrium  of  smallest  par- 
ticles, the  so-called  molecular  theories,  have  been 
gravely  threatened  by  the  progress  of  the  theory  of  the 
senses  and  of  space,  and  we  may  say  that  their  days 
are  numbered. 

I  have  shown  elsewhere*  that  the  musical  scale  is 

*  Compare  Mach's  Zur  Theorie  des  Gehdrorgans,  Vienna  Academy,  1863. 


ON  SYMMETRY,  105 

simply  a  species  of  space — a  space,  however,  of  only 
one  dimension,  and  that,  a  one-sided  one.  If,  now,  a 
person  who  could  only  hear,  should  attempt  to  develop 
a  conception  of  the  world  in  this,  his  linear  space,  he 
would  become  involved  in  many  difficulties,  as  his  space 
would  be  incompetent  to  comprehend  the  many  sides 
of  the  relations  of  reality.  But  is  it  any  more  justifi- 
able for  us,  to  attempt  to  force  the  whole  world  into  the 
space  of  our  eye,  in  aspects  in  which  it  is  not  accessi- 
ble to  the  eye  ?  Yet  this  is  the  dilemma  of  all  mo- 
lecular theories. 

We  possess,  however,  a  sense,  which,  with  respect 
to  the  scope  of  the  relations  which  it  can  comprehend, 
is  richer  than  any  other.  It  is  our  reason.  This  stands 
above  the  senses.  It  alone  is  competent  to  found  a 
permanent  and  sufficient  view  of  the  world.  The- 
mechanical  conception  of  the  world  has  performed 
wonders  since  Galileo's  time.  But  it  must  now  yield 
to  a  broader  view  of  things.  A  further  development  of 
this  idea  is  beyond  the  limits  of  my  present  purpose. 

One  more  point  and  I  have  done.  The  advice  of 
our  philosopher  to  restrict  ourselves  to  what  is  near 
at  hand  and  useful  in  our  researches,  which  finds  a 
kind  of  exemplification  in  the  present  cry  of  inquirers 
for  limitation  and  division  of  labor,  must  not  be  too 
slavishly  followed.  In  the  seclusion  of  our  closets,  we 
often  rack  our  brains  in  vain  to  fulfil  a  work,  the 
means  of  accomplishing  which  lies  before  our  very 
doors.  If  the  inquirer  must  be  perforce  a  shoemaker, 


io6  ON  SYMMETRY. 

tapping  constantly  at  his  last,  it  may  perhaps  be  per- 
mitted him  to  be  a  shoemaker  of  the  type  of  Hans 
Sachs,  who  did  not  deem  it  beneath  him  to  take  a 
look  now  and  then  at  his  neighbor's  work  and  to 
comment  on  the  latter's  doings. 

Let  this  be  my  apology,  therefore,  if  I  have  for- 
saken for  a  moment  to-day  the  last  of  my  specialty. 


ON  THE    FUNDAMENTAL  CONCEPTS 
OF  ELECTROSTATICS.* 


'T^HE  task  has  been  assigned  me  to  develop  before 
-•-  you  in  a  popular  manner  the  fundamental  quan- 
titative concepts  of  electrostatics — "quantity  of  elec- 
tricity," "potential,"  "capacity,"  and  so  forth.  It 
would  not  be  difficult,  even  within  the  brief  limits  of 
an  hour,  to  delight  the  eye  with  hosts  of  beautiful  ex- 
periments and  to  fill  the  imagination  with  numerous 
and  varied  conceptions.  But  we  should,  in  such  a 
case,  be  still  far  from  a  lucid  and  easy  grasp  of  the 
phenomena.  The  means  would  still  fail  us  for  repro- 
ducing the  facts  accurately  in  thought — a  procedure 
which  for  the  theoretical  and  practical  man  is  of  equal 
importance.  These  means  are  the  metrical  concepts  of 
electricity. 

As  long  as  the  pursuit  of  the  facts  of  a  given  pro- 
vince of  phenomena  is  in  the  hands  of  a  few  isolated 
investigators,  as  long  as  every  experiment  can  be  easily 
repeated,  the  fixing  of  the  collected  facts  by  provisional 

*  A  lecture  delivered  at  the  International  Electrical  Exhibition,  in  Vienna, 
on  September  4,  1883. 


io8  THE  CONCEPTS  OF  ELECTROSTA  TICS. 

description  is  ordinarily  sufficient.  But  the  case  is 
different  when  the  whole  world  must  make  use  of  the 
results  reached  by  many,  as  happens  when  the  sci- 
ence acquires  broader  foundations  and  scope,  and 
particularly  so  when  it  begins  to  supply  intellectual 
nourishment  to  an  important  branch  of  the  practical 
arts,  and  to  draw  from  that  province  in  return  stupen- 
dous empirical  results.  Then  the  facts  must  be  so 
described  that  individuals  in  all  places  and  at  all  times 
can,  from  a  few  easily  obtained  elements,  put  the  facts 
accurately  together  in  thought,  and  reproduce  them 
from  the  description.  This  is  done  with  the  help  of 
the  metrical  concepts  and  the  international  measures. 

The  work  which  was  begun  in  this  direction  in  the 
period  of  the  purely  scientific  development  of  the  sci- 
ence, especially  by  Coulomb  (1784),  Gauss  (1833),  and 
Weber  (1846),  was  powerfully  stimulated  by  the  re- 
quirements of  the  great  technical  undertakings  mani- 
fested since  the  laying  of  the  first  transatlantic  cable, 
and  brought  to  a  brilliant  conclusion  by  the  labors  of 
the  British  Association,  1861,  and  of  the  Paris  Con- 
gress, 1 88 1,  chiefly  through  the  exertions  of  Sir  Wil- 
liam Thomson. 

It  is  plain,  that  in  the  time  allotted  to  me  I  cannot 
conduct  you  over  all  the  long  and  tortuous  paths  which 
the  science  has  actually  pursued,  that  it  will  not  be 
possible  at  every  step  to  remind  you  of  all  the  little 
precautions  for  the  avoidance  of  error  which  the  early 
steps  have  taught  us.  On  the  contrary,  I  must  make 


THE  CONCEPTS  OF  ELECTROSTATICS.  109 

shift  with  the  simplest  and  rudest  tools.  I  shall  con- 
duct you  by  the  shortest  paths  from  the  facts  to  the 
ideas,  in  doing  which,  of  course,  it  will  not  be  possible 
to  anticipate  all  the  stray  and  chance  ideas  which  may 
and  must  arise  from  prospects  into  the  by-paths  which 

we  leave  untrodden. 

# 

*  * 

Here  are  two  small,  light  bodies  (Fig.  27)  of  equal 
size,   freely  suspended,  which  we   "electrify"  either 


O  Q 


o 


Fig.  27.  Fig.  28. 

by  friction  with  a  third  body  or  by  contact  with  a  body 
already  electrified.  At  once  a  repulsive  force  is  set 
up  which  drives  the  two  bodies  away  from  each  other 
in  opposition  to  the  action  of  gravity.  This  force  could 
accomplish  anew  the  same  mechanical  work  which 
was  expended  to  produce  it.* 

Coulomb,  now,  by  means  of  delicate  experiments 
with  the  torsion-balance,  satisfied  himself  that  if  the 
bodies  in  question,  say  at  a  distance  of  two  centime- 
tres, repelled  each  other  with  the  same  force  with 

*  If  the  two  bodies  were  oppositely  electrified  they  would  exert  attractions 
upon  each  other. 


no  THE  CONCEPTS  OF  ELECTROSTATICS. 

which  a  milligramme-weight  strives  to  fall  to  the 
ground,  at  half  that  distance,  or  at  one  centimetre, 
they  would  repel  each  other  with  the  force  of  four 
milligrammes,  and  at  double  that  distance,  or  at  four 
centimetres,  they  would  repel  each  other  with  the  force 
of  only  one-fourth  of  a  milligramme.  He  found  that 
the  electrical  force  acts  inversely  as  the  square  of  the 
distance. 

Let  us  imagine,  now,  that  we  possessed  some 
means  of  measuring  electrical  repulsion  by  weights, 
a  means  which  would  be  supplied,  for  example,  by  our 
electrical  pendulums;  then  we  could  make  the  follow- 
ing observation. 

The  body  A  (Fig.  28)  is  repelled  by  the  body  K  at 
a  distance  of  two  centimetres  with  a  force  of  one  milli- 
gramme. If  we  touch  A,  now,  with  an  equal  bod}'  B, 
the  half  of  this  force  of  repulsion  will  pass  to  the  body 
B ;  both  A  and  B,  now,  at  a  distance  of  two  centi- 
metres from  K,  are  repelled  only  with  the  force  of  one- 
half  a  milligramme.  But  both  together  are  repelled 
still  with  the  force  of  one  milligramme.  Hence,  the 
divisibility  of  electrical  force  among  bodies  in  contact  is 
a  fact.  It  is  a  useful,  but  by  no  means  a  necessary 
supplement  to  this  fact,  to  imagine  an  electrical  fluid 
present  in  the  body  A,  with  the  quantity  of  which  the 
electrical  force  varies,  and  half  of  which  flows  over  to 
B.  For,  in  the  place  of  the  new  physical  picture, 
thus,  an  old,  familiar  one  is  substituted,  which  moves 
spontaneously  in  its  wonted  courses. 


THE  CONCEPTS  OF  ELECTROSTATICS.  in 

Adhering  to  this  idea,  we  define  the  unit  of  electri- 
cal quantity,  according  to  the  now  almost  universally 
adopted  centimetre-gramme-second  (C.  G.  S.)  system, 
as  that  quantity  which  at  a  distance  of  one  centi- 
metre repels  an  equal  quantity  with  unit  of  force,  that 
is,  with  a  force  which  in  one  second  would  impart  to 
a  mass  of  one  gramme  a  velocity-increment  of  a  centi- 
metre. As  a  gramme  mass  acquires  through  the  action 
of  gravity  a  velocity-increment  of  about  981  centi- 
metres in  a  second,  accordingly,  a  gramme  is  attracted 
to  the  earth  with  981,  or,  in  round  numbers,  1000  units 
of  force  of  the  centimetre- gramme -second  system, 
while  a  milligramme-weight  would  strive  to  fall  to  the 
earth  with  approximately  the  unit  force  of  this  system. 

We  may  easily  obtain  by  this  means  a  clear  idea  of 
what  the  unit  quantity  of  electricity  is.  Two  small 
bodies,  K,  weighing  each  a  gramme,  are  hung  up  by 
vertical  threads,  five  metres  in  length  and  almost 
weightless,  so  as  to  touch  each  other.  If  the  two  bodies 
be  equally  electrified  and  move  apart  upon  electrifica- 
tion to  a  distance  of  one  centimetre,  their  charge  is  ap- 
proximately equivalent  to  the  electrostatic  unit  of  elec- 
tric quantity,  for  the  repulsion  then  holds  in  equilib- 
rium a  gravitational  force-component  of  approximately 
one  milligramme,  which  strives  to  bring  the  bodies  to- 
gether. 

Vertically  beneath  a  small  sphere  suspended  from 
the  equilibrated  beam  of  a  balance  a  second  sphere  is 
placed  at  a  distance  of  a  centimetre.  If  both  be  equally 


ii2          THE  CONCEPTS  OF  ELECTROSTATICS. 

electrified  the  sphere  suspended  from  the  balance  will 
be  rendered  apparently  lighter  by  the  repulsion.  If  by 
adding  a  weight  of  one  milligramme  equilibrium  is 
restored,  each  of  the  spheres  contains  in  round  num- 
bers the  electrostatic  unit  of  electrical  quantity. 

In  view  of  the  fact  that  the  same  electrical  bodies 
exert  at  different  distances  different  forces  upon  one 
another,  exception  might  be  taken  to  the  measure  of 
quantity  here  developed.  What  kind  of  a  quantity  is 
that  which  now  weighs  more,  and  now  weighs  less,  so 
to  speak  ?  But  this  apparent  deviation  from  the 
method  of  determination  commonly  used  in  practical 
life,  that  by  weight,  is,  closely  considered,  an  agree- 
ment. On  a  high  mountain  a  heavy  mass  also  is  less 
powerfully  attracted  to  the  earth  than  at  the  level  of 
the  sea,  and  if  it  is  permitted  us  in  our  determinations 
to  neglect  the  consideration  of  level,  it  is  only  because 
the  comparison  of  a  body  with  fixed  conventional 
weights  is  invariably  effected  at  the  same  level.  In 
fact,  if  we  were  to  make  one  of  the  two  weights  equi- 
librated on  our  balance  approach  sensibly  to  the  centre 
of  the  earth,  by  suspending  it  from  a  very  long  thread, 
as  Prof,  von  Jolly  of  Munich  suggested,  we  should 
make  the  gravity  of  that  weight,  its  heaviness,  propor- 
tionately greater. 

Let  us  picture  to  ourselves,  now,  two  different 
electrical  fluids,  a  positive  and  a  negative  fluid,  of  such 
nature  that  the  particles  of  the  one  attract  the  particles 
of  the  other  according  to  the  law  of  the  inverse  squares, 


THE  CONCEPTS  OF  ELECTROSTATICS.  113 

but  the  particles  of  the  same  fluid  repel  each  other  by 
the  same  law  ;  in  non-electrical  bodies  let  us  imagine 
the  two  fluids  uniformly  distributed  in  equal  quanti- 
ties, in  electric  bodies  one  of  the  two  in  excess;  in 
conductors,  further,  let  us  imagine  the  fluids  mobile, 
in  non-conductors  immobile  ;  having  formed  such  pic- 
tures, we  possess  the  conception  which  Coulomb  de- 
veloped and  to  which  he  gave  mathematical  precision. 
We  have  only  to  give  this  conception  free  play  in  our 
minds  and  we  shall  see  as  in  a  clear  picture  the  fluid 
particles,  say  of  a  positively  charged  conductor,  reced- 
ing from  one  another  as  far  as  they  can,  all  making 
for  the  surface  of  the  conductor  and  there  seeking  out 
the  prominent  parts  and  points  until  the  greatest  pos- 
sible amount  of  work  has  been  performed.  On  in- 
creasing the  size  of  the  surface,  we  see  a  dispersion, 
on  decreasing  its  size  we  see  a  condensation  of  the  par- 
ticles. In  a  second,  non- electrified  conductor  brought 
into  the  vicinity  of  the  first,  we  see  the  two  fluids  im- 
mediately separate,  the  positive  collecting  itself  on  the 
remote  and  the  negative  on  the  adjacent  side  of  its 
surface.  In  the  fact  that  this  conception  reproduces, 
lucidly  and  spontaneously,  all  the  data  which  arduous 
research  only  slowly  and  gradually  discovered,  is  con- 
tained its  advantage  and  scientific  value.  With  this, 
too,  its  value  is  exhausted.  We  must  not  seek  in  na- 
ture for  the  two  hypothetical  fluids  which  we  have 
added  as  simple  mental  adjuncts,  if  we  would  not  go 
astray.  Coulomb's  view  may  be  replaced  by  a  totally 


THE  CONCEPTS  OF  ELECTROSTATICS. 


different  one,  for  example,  by  that  of  Faraday,  and  the 
most  proper  course  is  always,  after  the  general  survey 
is  obtained,  to  go  back  to  the  actual  facts,  to  the  elec- 
trical forces. 

We  will  now  make  ourselves  familiar  with  the  con- 
cept of  electrical  quantity,  and  with  the  method  of 
measuring  or  estimating  it.  Imagine  a  common  Ley- 
den  jar  (Fig.  29),  the  inner  and  outer  coatings  of  which 
are  connected  together  by  means  of  two  common  me- 


Fig.  29.  Fig.  30. 

tallic  knobs  placed  about  a  centimetre  apart.  If  the 
inside  coating  be  charged  with  the  quantity  of  electri- 
city -|-  g,  on  the  outer  coating  a  distribution  of  the 
electricities  will  take  place.  A  positive  quantity  almost 
equal*  to  the  quantity  -\-  q  flows  off  to  the  earth,  while 
a  corresponding  quantity  • — q  is  still  left  on  the  outer 
coating.  The  knobs  of  the  jar  receive  their  portion  of 
these  quantities  and  when  the  quantity  q  is  sufficiently 
great  a  rupture  of  the  insulating  air  between  the  knobs, 

*The  quantity  which  flows  off  is  in  point  of  fact  less  than  q.  It  would  be 
equal  to  the  quantity  q  only  if  the  inner  coating  of  the  jar  were  wholly  encom- 
passed by  the  outer  coating. 


THE  CONCEPTS  OF  ELECTROSTA  TICS. 


accompanied  by  the  self-discharge  of  the  jar,  takes 
place.  For  any  given  distance  and  size  of  the  knobs, 
a  charge  of  a  definite  electric  quantity  q  is  always  ne- 
cessary for  the  spontaneous  discharge  of  the  jar. 

Let  us  insulate,  now,  the  outer  coating  of  a  Lane's 
unit  jar  L,  the  jar  just  described,  and  put  in  connex- 
ion with  it  the  inner  coating  of  a  jar  F  exteriorly  con- 
nected with  the  earth  (Fig.  30).  Every  time  that  L  is 
charged  with  -\-q,  a  like  quantity  -f  q  is  collected  on 
the  inner  coating  of  F,  and  the  spontaneous  discharge 
of  the  jar  Z,  which  is  now 
again  empty,  takes  place.  The 
number  of  the  discharges  of 
the  jar  L  furnishes  us,  thus, 
with  a  measure  of  the  quan- 
tity collected  in  the  jar  F,  and 
if  after  i,  2,  3, ...  spontaneous 
discharges  of  L  the  jar  F  is 
discharged,  it  is  evident  that  the  charge  of  F  has  been 
proportionately  augmented. 

Let  us  supply  now,  to  effect  the  spontaneous  dis- 
charge, the  jar  F  with  knobs  of  the  same  size  and 
at  the  same  distance  apart  as  those  of  the  jar  L  (Fig. 
31).  If  we  find,  then,  that  five  discharges  of  the  unit 
jar  take  place  before  one  spontaneous  discharge  of  the 
jar  F  occurs,  plainly  the  jar  F,  for  equal  distances  be- 
tween the  knobs  of  the  two  jars,  equal  striking  dis- 
tances, is  able  to  hold  five  times  the  quantity  of  elec- 


Fig.  31. 


n6 


THE  CONCEPTS  OF  ELECTROSTATICS. 


tricity  that  L  can,  that  is,  has  five  times  the  capacity 
of  L* 

We  will  now  replace  the  unit  jar  Z,  with  which  we 
measure  electricity,  so  to  speak,  into  the  jar  F,  by  a 
Franklin's  pane,  consisting  of  two  parallel  flat  metal 
plates  (Fig.  32),  separated  only  by  air.  If  here,  for 
example,  thirty  spontaneous  discharges  of  the  pane  are 
sufficient  to  fill  the  jar,  ten  discharges  will  be  found 


Fig.  33. 

sufficient  if  the  air-space  between  the  two  plates  be 
filled  with  a  cake  of  sulphur.  Hence,  the  capacity 
of  a  Franklin's  pane  of  sulphur  is  about  three  times 
greater  than  that  of  one  of  the  same  shape  and  size 

*  Rigorously,  of  course,  this  is  not  correct.  First,  it  is  to  be  noted  that  the 
jar  L  is  discharged  simultaneously  with  the  electrode  of  the  machine.  The 
jar  F,  on  the  other  hand,  is  always  discharged  simultaneously  with  the  outer 
coating  of  the  jar  L.  Hence,  if  we  call  the  capacity  of  the  electrode  of  the 
machine  E,  that  of  the  unit  jar  L,  that  of  the  outer  coating  of  L,  A,  and  that  of 
the  principal  jar  F,  then  this  equation  would  exist  for  the  example  in  the  text: 
(f+  A)/(L  +  E)  =  5.  A  cause  of  further  departure  from  absolute  exactness  is 
the  residual  charge. 


THE  CONCEPTS  OF  ELECTROSTATICS.  117 

made  of  air,  or,  as  it  is  the  custom  to  say,  the  specific 
inductive  capacity  of  sulphur  (that  of  air  being  taken 
as  the  unit)  is  about  3.*  We  are  here  arrived  at  a 
very  simple  fact,  which  clearly  shows  us  the  signifi- 
cance of  the  number  called  dielectric  constant,  or  speci- 
fic inductive  capacity,  the  knowledge  of  which  is  so  im- 
portant for  the  theory  of  submarine  cables. 

Let  us  consider  a  jar  A,  which  is  charged  with  a 
certain  quantity  of  electricity.  We  can  discharge  the 
jar  directly.  But  we  can  also  discharge  the  jar  A 


A 

Fig.  33-  Fig.  34- 

(Fig.  33)  partly  into  a  jar  Bt  by  connecting  the  two 
outer  coatings  with  each  other.  In  this  operation  a 
portion  of  the  quantity  of  electricity  passes,  accompa- 
nied by  sparks,  into  the  jar  B,  and  we  now  find  both 
jars  charged. 

It  may  be  shown  as  follows  that  the  conception  of 

*  Making  allowance  for  the  corrections  indicated  in  the  preceding  foot- 
note, I  have  obtained  for  the  dielectric  constant  of  sulphur  the  number  3.2, 
which  agrees  practically  with  the  results  obtained  by  more  delicate  methods. 
For  the  highest  attainable  precision  one  should  by  rights  immerse  the  two 
plates  of  the  condenser  first  wholly  in  air  and  then  wholly  in  sulphur,  if  the 
ratio  of  the  capacities  is  to  correspond  to  the  dielectric  constant.  In  point  of 
fact,  however,  the  error  which  arises  from  inserting  simply  a  plate  of  sulphur 
that  exactly  fills  the  space  between  the  two  plates,  is  of  no  consequence. 


n8          THE  CONCEPTS  OF  ELECTROSTATICS. 

a  constant  quantity  of  electricity  can  be  regarded  as 
the  expression  of  a  pure  fact.  Picture  to  yourself  any 
sort  of  electrical  conductor  (Fig.  34) ;  cut  it  up  into  a 
large  number  of  small  pieces,  and  place  these  pieces  by 
means  of  an  insulated  rod  at  a  distance  of  one  centi- 
metre from  an  electrical  body  which  acts  with  unit  of 
force  on  an  equal  and  like-constituted  body  at  the 
same  distance.  Take  the  sum  of  the  forces  which 
this  last  body  exerts  on  the  single  pieces  of  the  con- 
ductor. The  sum  of  these  forces  will  be  the  quantity 
of  electricity  on  the  whole  conductor.  It  remains  the 
same,  whether  we  change  the  form  and  the  size  of  the 
conductor,  or  whether  we  bring  it  near  or  move  it 
away  from  a  second  electrical  conductor,  so  long  as  we 
keep  it  insulated,  that  is,  do  not  discharge  it. 

A  basis  of  reality  for  the  notion  of  electric  quan- 
tity seems  also  to  present  itself  from  another  quar- 
ter. If  a  current,  that  is,  in  the  usual  view,  a  definite 
quantity  of  electricity  per  second,  is  sent  through  a 
column  of  acidulated  water ;  in  the  direction  of  the 
positive  stream,  hydrogen,  but  in  the  opposite  direc- 
tion, oxygen  is  liberated  at  the  extremities  of  the  col- 
umn. For  a  given  quantity  of  electricity  a  given  quan- 
tity of  oxygen  appears.  You  may  picture  the  column 
of  water  as  a  column  of  hydrogen  and  a  column  of 
oxygen,  fitted  into  each  other,  and  may  say  the  electric 
current  is  a  chemical  current  and  vice  versa.  Although 
this  notion  is  more  difficult  to  adhere  to  in  the  field  of 
statical  electricity  and  with  non-decomposable  con- 


THE  CONCEPTS  OF  ELECTROSTA  TICS 


ng 


ductors,  its  further  development  is  by  no  means  hope- 
less. 

The  concept  quantity  of  electricity,  thus,  is  not  so 
aerial  as  might  appear,  but  is  able  to  conduct  us  with 
certainty  through  a  multitude  of  varied  phenomena, 
and  is  suggested  to  us  by  the  facts  in  almost  palpable 
form.  We  can  collect  electrical  force  in  a  body,  meas- 
ure it  out  with  one  body 
into  another,  carry  it 
over  from  one  body  into 
another,  just  as  we  can 
collect  a  liquid  in  a  ves- 
sel, measure  it  out  with 
one  vessel  into  another, 
or  pour  it  from  one  into 
another. 

For  the  analysis  of 
mechanical  phenomena, 
a  metrical  notion,  de- 
rived from  experience, 
and  bearing  the  designation  work,  has  proved  itself 
useful.  A  machine  can  be  set  in  motion  only  when 
the  forces  acting  on  it  can  perform  work. 

Let  us  consider,  for  example,  a  wheel  and  axle 
(Fig.  35)  having  the  radii  i  and  2  metres,  loaded  re- 
spectively with  the  weights  2  and  i  kilogrammes.  On 
turning  the  wheel  and  axle,  the  i  kilogramme-weight, 
let  us  say,  sinks  two  metres,  while  the  2  kilogramme- 
weight  rises  one  metre.  On  both  sides  the  product 


Fig.  35- 


izo  THE  CONCEPTS  OF  ELECTROSTATICS. 

KGR.         M.  KGR.          M. 

1X2=2X1. 

is  equal.  So  long  as  this  is  so,  the  wheel  and  axle  will 
not  move  of  itself.  But  if  we  take  such  loads,  or  so 
change  the  radii  of  the  wheels,  that  this  product  (kgr. 
X  metre)  on  displacement  is  in  excess  on  one  side, 
that  side  will  sink.  As  we  see,  this  product  is  charac- 
teristic for  mechanical  events,  and  for  this  reason  has 
been  invested  with  a  special  name,  work. 

In  all  mechanical  processes,  and  as  all  physical 
processes  present  a  mechanical  side,  in  all  physical 
processes,  work  plays  a  determinative  part.  Electrical 
forces,  also,  produce  only  changes  in  which  work  is  per- 
formed. To  the  extent  that  forces  come  into  play  in 
electrical  phenomena,  electrical  phenomena,  be  they 
what  they  may,  extend  into  the  domain  of  mechanics 
and  are  subject  to  the  laws  which  hold  in  this  do- 
main. The  universally  adopted  measure  of  work, 
now,  is  the  product  of  the  force  into  the  distance 
through  which  it  acts,  and  in  the  C.  G.  S.  system,  the 
unit  of  work  is  the  action  through  one  centimetre  of 
a  force  which  would  impart  in  one  second  to  a 
gramme-mass  a  velocity-increment  of  one  centimetre, 
that  is,  in  round  numbers,  the  action  through  a  centi- 
metre of  a  pressure  equal  to  the  weight  of  a  milli- 
gramme. From  a  positively  charged  body,  electricity, 
yielding  to  the  force  of  repulsion  and  performing  work, 
flows  off  to  the  earth,  providing  conducting  connexions 
exist.  To  a  negatively  charged  body,  on  the  other 


THE  CONCEPTS  OF  ELECTROSTATICS.  121 

hand,  the  earth  under  the  same  circumstances  gives 
off  positive  electricity.  The  electrical  work  possible 
in  the  interaction  of  a  body  with  the  earth,  character- 
ises the  electrical  condition  of  that  body.  We  will  call 
the  work  which  must  be  expended  on  the  unit  quantity 
of  positive  electricity  to  raise  it  from  the  earth  to  the 
body  K  the  potential  of  the  body  K* 

We  ascribe  to  the  body  K  in  the  C.  G.  S.  system 
the  potential  -{-  i,  if  we  must  expend  the  unit  of  work 
to  raise  the  positive  electrostatic  unit  of  electric  quan- 
tity from  the  earth  to  that  body ;  the  potential  — i,  if 
we  gain  in  this  procedure  the  unit  of  work  ;  the  poten- 
tial 0,  if  no  work  at  all  is  performed  in  the  operation. 

The  different  parts  of  one  and  the  same  electrical 
conductor  in  electrical  equilibrium  have  the  same  po- 
tential, for  otherwise  the  electricity  would  perform 
work  and  move  about  upon  the  conductor,  and  equili- 
brium would  not  have  existed.  Different  conductors  of 
equal  potential,  put  in  connexion  with  one  another,  do 
not  exchange  electricity  any  more  than  bodies  of  equal 
temperature  in  contact  exchange  heat,  or  in  connected 
vessels,  in  which  the  same  pressures  exist,  liquids 

*  As  this  definition  in  its  simple  form  is  apt  to  give  rise  to  misunderstand- 
ings, elucidations  are  usually  added  to  it.  It  is  clear  that  we  cannot  lift  a 
quantity  of  electricity  to  K,  without  changing  the  distribution  on  AT  and  the 
potential  on  K.  Hence,  the  charges  on  K  must  be  conceived  as  fixed,  and  so 
small  a  quantity  raised  that  no  appreciable  change  is  produced  by  it.  Taking 
the  work  thus  expended  as  many  times  as  the  small  quantity  in  question  is 
contained  in  the  unit  of  quantity,  we  shall  obtain  the  potential.  The  poten- 
tial of  a  body  A' may  be  briefly  and  precisely  defined  as  follows  :  If  we  expend 
the  element  of  work  dW\.o  raise  the  element  of  positive  quantity  dQ  from  the 
earth  to  the  conductor,  the  potential  of  a  conductor  AT  will  be  given  by  y= 
dWIdQ. 


122  THE  CONCEPTS  OF  ELECTROSTATICS. 

flow  from  one  vessel  to  the  other.  Exchange  of  elec- 
tricity takes  place  only  between  conductors  of  different 
potentials,  but  in  conductors  of  given  form  and  posi- 
tion a  definite  difference  of  potential  is  necessary  for 
a  spark,  which  pierces  the  insulating  air,  to  pass 
between  them. 

On  being  connected,  every  two  conductors  assume 
at  once  the  same  potential.  With  this  the  means 
is  given  of  determining  the  potential  of  a  conductor 
through  the  agency  of  a  second  conductor  expressly 
adapted  to  the  purpose  called  an  electrometer,  just  as 
we  determine  the  temperature  of  a  body  with  a  ther- 
mometer. The  values  of  the  potentials  of  bodies  ob- 
tained in  this  way  simplify  vastly  our  analysis  of  their 
electrical  behavior,  as  will  be  evident  from  what  has 
been  said. 

Think  of  a  positively  charged  conductor.  Double 
all  the  electrical  forces  exerted  by  this  conductor  on  a 
point  charged  with  unit  quantity,  that  is,  double  the 
quantity  at  each  point,  or  what  is  the  same  thing, 
double  the  total  charge.  Plainly,  equilibrium  still  sub- 
sists. But  carry,  now,  the  positive  electrostatic  unit 
towards  the  conductor.  Everywhere  we  shall  have  to 
overcome  double  the  force  of  repulsion  we  did  before, 
everywhere  we  shall  have  to  expend  double  the  work. 
By  doubling  the  charge  of  the  conductor  a  double  po- 
tential has  been  produced.  Charge  and  potential  go 
hand  in  hand,  are  proportional.  Consequently,  call- 
ing the  total  quantity  of  electricity  of  a  conductor  Q 


THE  CONCEPTS  OF  ELECTROSTATICS.          123 

and  its  potential  V,  we  can  write  :  Q=  CV,  where  C 
stands  for  a  constant,  the  import  of  which  will  be  un- 
derstood simply  from  noting  that  C=  Q/V.  *  But  the 
division  of  a  number  representing  the  units  of  quan- 
tity of  a  conductor  by  the  number  representing  its 
units  of  potential  tells  us  the  quantity  which  falls  to 
the  share  of  the  unit  of  potential.  Now  the  number 
C  here  we  call  the  capacity  of  a  conductor,  and  have 
substituted,  thus,  in  the  place  of  the  old  relative  de- 
termination of  capacity,  an  absolute  determination,  f 

In  simple  cases  the  connexion  between  charge,  po- 
tential, and  capacity  is  easily  ascertained.  Our  con- 
ductor, let  us  say,  is  a  sphere  of  radius  r,  suspended 
free  in  a  large  body  of  air.  There  being  no  other  con- 
ductors in  the  vicinity,  the  charge  q  will  then  distribute 
itself  uniformly  upon  the  surface  of  the  sphere,  and 
simple  geometrical  considerations  yield  for  its  poten- 
tial the  expression  V=q/r.  Hence,  qlV=r-}  that  is, 
the  capacity  of  a  sphere  is  measured  by  its  radius,  and 

*  In  this  article  the  solidus  or  slant  stroke  is  used  for  the  usual  fractional 
sign  of  division.  Where  plus  or  minus  signs  occur  in  the  numerator  or  de- 
nominator, brackets  or  a  vinculum  is  used. —  Tr. 

t  A  sort  of  agreement  exists  between  the  notions  of  thermal  and  electrical 
capacity,  but  the  difference  between  the  two  ideas  also  should  be  carefully 
borne  in  mind.  The  thermal  capacity  of  a  body  depends  solely  upon  that  body 
itself.  The  electrical  capacity  of  a  body  AT  is  influenced  by  all  bodies  in  its 
vicinity,  inasmuch  as  the  charge  of  these  bodies  is  able  to  alter  the  potential 
of  K.  To  give,  therefore,  an  unequivocal  significance  to  the  notion  of  the  ca- 
pacity (C)  of  a  body  K,  Cis  defined  as  the  relation  Q  /  V  for  the  body  A" in  a 
certain  given  position  of  all  neighboring  bodies,  and  during  connexion  of  all 
neighboring  conductors  with  the  earth.  In  practice  the  situation  is  much 
simpler.  The  capacity,  for  example,  of  a  jar,  the  inner  coating  of  which  is 
almost  enveloped  by  its  outer  coating,  communicating  with  the  ground,  is  not 
sensibly  affected  by  charged  or  uncharged  adjacent  conductors. 


I24  THE  CONCEPTS  OF  ELECl^ROSTATICS. 

in  the  C.  G.  S.  system  in  centimetres.*  It  is  clear 
also,  since  a  potential  is  a  quantity  divided  by  a  length, 
that  a  quantity  divided  by  a  potential  must  be  a  length. 
Imagine  (Fig.  36)  a  jar  composed  of  two  concen- 
tric conductive  spherical  shells  of  the  radii  r  and  r^, 
having  only  air  between  them.  Connecting  the  out- 
side sphere  with  the  earth,  and  charging  the  inside 
sphere  by  means  of  a  thin,  insulated  wire  passing 
through  the  first,  with  the  quantity  Q,  we  shall  have 
V=(r^ — /O/Cfj  r)  Q,  and  for  the  capacity  in  this  case 

(.rir^)/(.ri — r)»  or>  *°  ta^e 
a  specific  example,  if  r=i6 
and  ri=ig,  a  capacity  of 
about  100  centimetres. 

We  shall  now  use  these 
simple  cases  for  illustrat- 
ing the  principle  by  which 
capacity  and  potential  are 
determined.  First,  it  is 

Fig.  36. 

clear  that  we  can  use  the 

jar  composed  of  concentric  spheres  with  its  known  ca- 
pacity as  our  unit  jar  and  by  means  of  this  ascertain, 
in  the  manner  above  laid  down,  the  capacity  of  any 
given  jar  f.  We  find,  for  example,  that  37  discharges 
of  this  unit  jar  of  the  capacity  100,  just  charges  the 


*  These  formulae  easily  follow  from  Newton's  theorem  that  a  homogeneous 
spherical  shell,  whose  elements  obey  the  law  of  the  inverse  squares,  exerts  no 
force  whatever  on  points  within  it  but  acts  on  points  without  as  if  the  whole 
mass  were  concentrated  at  its  centre.  The  formulae  next  adduced  also  flow 
from  this  proposition. 


THE  CONCEPTS  OF  ELECTROSTATICS. 


125 


jar  investigated  at  the  same  striking  distance,  that  is, 
at  the  same  potential.  Hence,  the  capacity  of  the  jar 
investigated  is  3700  centimetres.  The  large  battery 
of  the  Prague  physical  laboratory,  which  consists  of 
sixteen  such  jars,  all  of  nearly  equal  size,  has  a  capa- 
city, therefore,  of  something  like  50,000  centimetres, 
or  the  capacity  of  a  sphere,  a  kilometre  in  diameter, 
freely  suspended  in  atmospheric  space.  This  remark 

1 


Fig.  37- 


distinctly  shows  us  the  great  superiority  which  Leyden 
jars  possess  for  the  storage  of  electricity  as  compared 
with  common  conductors.  In  fact,  as  Faraday  pointed 
out,  jars  differ  from  simple  conductors  mainly  by  their 
great  capacity. 

For  determining  potential,  imagine  the  inner  coat- 
ing of  a  jar  f,  the  outer  coating  of  which  communi- 
cates with  the  ground,  connected  by  a  long,  thin  wire 
with  a  conductive  sphere  K  placed  free  in  a  large  at- 
mospheric space,  compared  with  whose  dimensions 


ia6          THE  CONCEPTS  OF  ELECTROSTATICS. 

the  radius  of  the  sphere  vanishes.  (Fig.  37.)  The 
jar  and  the  sphere  assume  at  once  the  same  potential. 
But  on  the  surface  of  the  sphere,  if  that  be  sufficiently 
far  removed  from  all  other  conductors,  a  uniform  layer 
of  electricity  will  be  found.  If  the  sphere,  having  the 
radius  r,  contains  the  charge  q,  its  potential  is  V^=qjr. 
If  the  upper  half  of  the  sphere  be  severed  from  the 
lower  half  and  equilibrated  on  a  balance  with  one  of 
whose  beams  it  is  connected  by  silk  threads,  the  upper 
half  will  be  repelled  from  the  lower  half  with  the  force 
P=g*/8r2  =  %F'2.  This  repulsion  P  may  be  counter- 
balanced by  additional  weights  placed  on  the  beam- 
end,  and  so  ascertained.  The  potential  is  then  V= 


That  the  potential  is  proportional  to  the  square 
root  of  the  force  is  not  difficult  to  see.  A  doubling  or 
trebling  of  the  potential  means  that  the  charge  of  all 
the  parts  is  doubled  or  trebled  ;  hence  their  combined 
power  of  repulsion  quadrupled  or  nonupled. 

Let  us  consider  a  special  case.  I  wish  to  produce 
the  potential  40  on  the  sphere.  What  additional  weight 
must  I  give  to  the  half  sphere  in  grammes  that  the 
force  of  repulsion  shall  maintain  the  balance  in  exact 
equilibrium  ?  As  a  gramme  weight  is  approximately 

*The  energy  of  a  sphere  of  radius  r  charged  with  the  quantity  q  is 
%  (<fi  /r)-  I'  the  radius  increase  by  the  space  dr  a  loss  of  energy  occurs,  and 
the  work  done  is  %(ql/  r2)dr.  Letting/  denote  the  uniform  electrical  pres- 
sure on  unit  of  surface  of  the  sphere,  the  work  done  is  also  4  rtTtpdr.  Hence 
/  =  (i/8r27r)(jr2/r2).  Subjected  to  the  same  superficial  pressure  on  all  sides, 
say  in  a  fluid,  our  half  sphere  would  be  an  equilibrium.  Hence  we  must  make 
the  pressure/  act  on  the  surface  of  the  great  circle  to  obtain  the  effect  on  the 
balance,  which  is  rt  np  =  ys(9y  rt)=yt  VZ. 


THE  CONCEPTS  OF  ELECTROSTATICS.  127 

equivalent  to  1000  units  of  force,  we  have  only  the 
following  simple  example  to  work  out  :  40  X  4°  =  8  X 
i coo..*,  where  x  stands  for  the  number  of  grammes. 
In  round  numbers  we  get  x  =  0.2  gramme.  I  charge 
the  jar.  The  balance  is  deflected ;  I  have  reached, 
or  rather  passed,  the  potential  40,  and  you  see  when  I 
discharge  the  jar  the  associated  spark.* 

The  striking  distance  between  the  knobs  of  a  ma- 
chine increases  with  the  difference  of  the  potential, 
although  not  proportionately  to  that  difference.  The 
striking  distance  increases  faster  than  the  potential 
difference.  For  a  distance  between  the  knobs  of  one 
centimetre  on  this  machine  the  difference  of  potential 
is  no.  It  can  easily  be  increased  tenfold.  Of  the 
tremendous  differences  of  potential  which  occur  in 
nature  some  idea  may  be  obtained  from  the  fact  that 
the  striking  distances  of  lightning  in  thunder-storms 
is  counted  by  miles.  The  differences  of  potential  in 
galvanic  batteries  are  considerably  smaller  than  those 
of  our  machine,  for  it  takes  fully  one  hundred  elements 
to  give  a  spark  of  microscopic  striking  distance. 

* 
*  * 

We  shall  now  employ  the  ideas  reached  to  shed 
some  light  upon  another  important  relation  between 

*  The  arrangement  described  is  for  several  reasons  not  fitted  for  the  actual 
measurement  of  potential.  Thomson's  absolute  electrometer  is  based  upon 
an  ingenious  modification  of  the  electrical  balance  of  Harris  and  Volta.  Of 
two  large  plane  parallel  plates,  one  communicates  with  the  earth,  while  the 
other  is  brought  to  the  potential  to  be  measured.  A  small  movable  superficial 
portion  f  of  this  last  hangs  from  the  balance  for  the  determination  of  the 
attraction  P.  The  distance  of  the  plates  from  each  other  being  D  we  get  V= 


i28  THE  CONCEPTS  OF  ELECTROSTATICS, 

electrical  and  mechanical  phenomena.  We  shall  in- 
vestigate what  is  the  potential  energy  ',  or  the  store  of 
•work,  contained  in  a  charged  conductor,  for  example, 
in  a  jar. 

If  we  bring  a  quantity  of  electricity  up  to  a  con- 
ductor, or,  to  speak  less  pictorially,  if  we  generate  by 
work  electrical  force  in  a  conductor,  this  force  is  able 
to  produce  anew  the  work  by  which  it  was  generated. 
How  great,  now,  is  the  energy  or  capacity  for  work  of 
a  conductor  of  known  charge  Q  and  known  poten- 
tial F? 

Imagine  the  given  charge  Q  divided  into  very  small 
parts  q,  q^  q^  .  .  .  .,  and  these  little  parts  successively 
carried  up  to  the  conductor.  The  first  very  small 
quantity  q  is  brought  up  without  any  appreciable  work 
and  produces  by  its  presence  a  small  potential  V,.  To 
bring  up  the  second  quantity,  accordingly,  we  must  do 
the  work  q,  Vn  and  similarly  for  the  quantities  which 
follow  the  work  q,^,,,  qn,Vlin  and  so  forth.  Now, 
as  the  potential  rises  proportionately  to  the  quantities 
added  until  the  value  V  is  reached,  we  have,  agree- 
ably to  the  graphical  representation  of  Fig.  38,  for  the 
total  work  performed, 


which  corresponds  to  the  total  energy  of  the  charged 
conductor.  Using  the  equation  Q  =  C  V,  where  C 
stands  for  capacity,  we  also  have, 


or 


THE  CONCEPTS  OF  ELECTROSTA  TICS. 


129 


It  will  be  helpful,  perhaps,  to  elucidate  this  idea 
by  an  analogy  from  the  province  of  mechanics.  If  we 
pump  a  quantity  of  liquid,  Q,  gradually  into  a  cylin- 
drical vessel  (Fig.  39),  the  level  of  the  liquid  in  the 
vessel  will  gradually  rise.  The  more  we  have  pumped 
in,  the  greater  the  pressure  we  must  overcome,  or  the 
higher  the  level  to  which  we  must  lift  the  liquid.  The 
stored-up  work  is  rendered  again  available  when  the 
heavy  liquid  Q,  which  reaches  up  to  the  level  h,  flows 
out.  This  work  W  corresponds  to  the  fall  of  the  whole 


Q 

Fig-  38.  Fig.  39. 

liquid  weight  Q,  through  the  distance  h/2  or  through 
the  altitude  of  its  centre  of  gravity.     We  have 


Further,  since   Q  =  K  h,  or  since  the  weight  of  the 
liquid  and  the  height  h  are  proportional,  we  get  also 


As  a  special  case  let  us  consider  our  jar.  Its  ca- 
pacity is  (7—3700,  its  potential  V=  1  10  ;  accordingly, 
its  quantity  Q=  CV=  407,000  electrostatic  units  and 
its  energy  W  =%  QV=  22,385,000  C.  G.  S.  units  of 
work. 


!30          THE  CONCEPTS  OF  ELECTROSTATICS. 

The  unit  of  work  of  the  C.  G.  S.  system  is  not  readily 
appreciable  by  the  senses,  nor  does  it  well  admit  of 
representation,  as  we  are  accustomed  to  work  with 
weights.  Let  us  adopt,  therefore,  as  our  unit  of  work 
the  gramme-centimetre,  or  the  gravitational  pressure 
of  a  gramme-weight  through  the  distance  of  a  centi- 
metre, which  in  round  numbers  is  1000  times  greater 
than  the  unit  assumed  above ;  in  this  case,  our  numer- 
ical result  will  be  approximately  1000  times  smaller. 
Again,  if  we  pass,  as  more  familiar  in  practice,  to  the 
kilogramme-metre  as  our  unit  of  work,  our  unit,  the 
distance  being  increased  a  hundred  fold,  and  the  weight 
a  thousand  fold,  will  be  100,000  times  larger.  The 
numerical  result  expressing  the  work  done  is  in  this 
case  100,000  times  less,  being  in  round  numbers  0.22 
kilogramme-metre.  We  can  obtain  a  clear  idea  of  the 
work  done  here  by  letting  a  kilogramme-weight  fall  22 
centimetres. 

This  amount  of  work,  accordingly,  is  performed  on 
the  charging  of  the  jar,  and  on  its  discharge  appears 
again,  according  to  the  circumstances,  partly  as  sound, 
partly  as  a  mechanical  disruption  of  insulators,  partly 
as  light  and  heat,  and  so  forth. 

The  large  battery  of  the  Prague  physical  labora- 
tory, with  its  sixteen  jars  charged  to  equal  potentials, 
furnishes,  although  the  effect  of  the  discharge  is  im- 
posing, a  total  amount  of  work  of  only  three  kilo- 
gramme-metres. 


THE  CONCEPTS  OF  ELECTROSTA  TICS.  i3x 

In  the  development  of  the  ideas  above  laid  down 
we  are  not  restricted  to  the  method  there  pursued  ;  in 
fact,  that  method  was  selected  only  as  one  especially 
fitted  to  familiarise  us  with  the  phenomena.  On  the 
contrary,  the  connexion  of  the  physical  processes  is  so 
multifarious  that  we  can  come  at  the  same  event  from 
very  different  directions.  Particularly  are  electrical 
phenomena  connected  with  all  other  physical  events  ; 
and  so  intimate  is  this  connexion  that  we  might  justly 
call  the  study  of  electricity  the  theory  of  the  general 
connexion  of  physical  processes. 

With  respect  to  the  principle  of  the  conservation 
of  energy  which  unites  electrical  with  mechanical  phe- 
nomena, I  should  like  to  point  out  briefly  two  ways  of 
following  up  the  study  of  this  connexion. 

A  few  years  ago  Professor  Rosetti,  taking  an  in- 
fluence-machine, which  he  set  in  motion  by  means  of 
weights  alternately  in  the  electrical  and  non-electrical 
condition  with  the  same  velocities,  determined  the 
mechanical  work  expended  in  the  two  cases  and  was 
thus  enabled,  after  deducting  the  work  of  friction,  to 
ascertain  the  mechanical  work  consumed  in  the  devel- 
opment of  the  electricity. 

I  myself  have  made  this  experiment  in  a  modified, 
and,  as  I  think,  more  advantageous  form.  Instead 
of  determining  the  work  of  friction  by  special  trial,  I 
arranged  my  apparatus  so  that  it  was  eliminated  of  it- 
self in  the  measurement  and  could  consequently  be 
neglected.  The  so-called  fixed  disk  of  the  machine,  the 


132  THE  CONCEPTS  OF  ELECTROSTATICS. 

axis  of  which  is  placed  vertically,  is  suspended  some- 
what like  a  chandelier  by  three  vertical  threads  of 
equal  lengths  /  at  a  distance  r  from  the  axis.  Only 
when  the  machine  is  excited  does  this  fixed  disk,  which 
represents  a  Prony's  brake,  receive,  through  its  recip- 
rocal action  with  the  rotating  disk,  a  deflexion  a  and  a 
moment  of  torsion  which  is  expressed  by  D  =(Prz  /l}a, 
where  P  is  the  weight  of  the  disk.*  The  angle  a  is 
determined  by  a  mirror  set  in  the  disk.  The  work  ex- 
pended in  n  rotations  is  given  by  znnD. 

If  we  close  the  machine,  as  Rosetti  did,  we  obtain 
a  continuous  current  which  has  all  the  properties  of  a 
very  weak  galvanic  current;  for  example,  it  produces  a 
deflexion  in  a  multiplier  which  we  interpose,  and  so 
forth.  We  can  directly  ascertain,  now,  the  mechanical 
work  expended  in  the  maintenance  of  this  current. 

If  we  charge  a  jar  by  means  of  a  machine,  the  en- 
ergy of  the  jar  employed  in  the  production  of  sparks, 
in  the  disruption  of  the  insulators,  etc.,  corresponds 
to  a  part  only  of  the  mechanical  work  expended,  a 
second  part  of  it  being  consumed  in  the  arc  which 
forms  the  circuit,  f  This  machine,  with  the  interposed 
jar,  affords  in  miniature  a  picture  of  the  transference 

*This  moment  of  torsion  needs  a  supplementary  correction,  on  account  of 
the  vertical  electric  attraction  of  the  excited  disks.  This  is  done  by  changing 
the  weight  of  the  disk  by  means  of  additional  weights  and  by  making  a  second 
reading  of  the  angles  of  deflexion. 

tThe  jar  in  our  experiment  acts  like  an  accumulator,  being  charged  by  a 
dynamo  machine.  The  relation  which  obtains  between  the  expended  and  the 
available  work  may  be  gathered  from  the  following  simple  exposition.  A 
Holtz  machine  If  (Fig.  40)  is  charging  a  unit  jar  L,  which  after  n  discharges 
of  quantity  j  and  potential  v,  charges  the  jar  /?  with  the  quantity  Q  at  the  po- 


THE  CONCEPTS  OF  ELECTROSTATICS. 


133 


of  force,  or  more  properly  of  work.  And  in  fact  nearly 
the  same  laws  hold  here  for  the  economical  coefficient 
as  obtain  for  large  dynamo-machines. 

Another  means  of  investigating  electrical  energy  is 
by  its  transformation  into  heat.  A  long  time  ago 
(1838),  before  the  mechanical  theory  of  heat  had  at- 
tained its  present  popularity,  Riess  performed  expe- 
riments in  this  field  with  the  help  of  his  electrical 
air-thermometer  or  thermo- 
electrometer. 

If  the  discharge  be  con- 
ducted through  a  fine  wire 
passing  through  the  globe  of 
the  air-thermometer,  a  devel- 
opment of  heat  is  observed 
proportional  to  the  expression 
above  -  discussed  W=  \QV. 
Although  the  total  energy  has 
not  yet  been  transformed 
into  measurable  heat  by  this 
means,  inasmuch  as  a  portion 
is  left  behind  in  the  spark  in  the  air  outside  the  ther- 
mometer, still  everything  tends  to  show  that  the  total 

tential  V.  The  energy  of  the  unit-jar  discharges  is  lost  and  that  of  the  jar  F 
alone  is  left.  Hence  the  ratio  of  the  available  work  to  the  total  work  ex- 
pended is 

and  as  Q  =  nq,  also 


It,  now,  we  interpose  no  unit  jar,  still  the  parts  of  the  machine  and  the  wires 
of  conduction  are  themselves  virtually  such  unit  jars  and  the  formula  still 
subsists  V/  V  +  2  v,  in  which  2  v  represents  the  sum  of  all  the  successively  in- 
troduced differences  of  potential  in  the  circuit  of  connexion. 


Fig.  40- 


i34          THE  CONCEPTS  OF  ELECTROSTATICS. 

heat  developed  in  all  parts  of  the  conductor  and  along 
all  the  paths  of  discharge  is  the  equivalent  of  the  work 


It  is  not  important  here  whether  the  electrical  en- 
ergy is  transformed  all  at  once  or  partly,  by  degrees. 
For  example,  if  of  two  equal  jars  one  is  charged  with 
the  quantity  Q  at  the  potential  Fthe  energy  present 
\B  ^QV.  If  the  first  jar  be  discharged  into  the  second, 
V,  since  the  capacity  is  now  doubled,  falls  to  F/2. 
Accordingly,  the  energy  \  Q  V  remains,  while  \QV\s 
transformed  in  the  spark  of  discharge  into  heat.  The 
remainder,  however,  is  equally  distributed  between 
the  two  jars  so  that  each  on  discharge  is  still  able  to 
transform  \  Q  V  into  heat. 

* 
*  * 

We  have  here  discussed  electricity  in  the  limited 
phenomenal  form  in  which  it  was  known  to  the  in- 
quirers before  Volta,  and  which  has  been  called,  per- 
haps not  very  felicitously,  "statical  electricity."  It  is 
evident,  however,  that  the  nature  of  electricity  is  every- 
where one  and  the  same  ;  that  a  substantial  difference 
between  statical  and  galvanic  electricity  does  not  exist. 
Only  the  quantitative  circumstances  in  the  two  pro- 
vinces are  so  widely  different  that  totally  new  aspects 
of  phenomena  may  appear  in  the  second,  for  example, 
magnetic  effects,  which  in  the  first  remained  unnoticed, 
whilst,  vice  versa,  in  the  second  field  statical  attrac- 
tions and  repulsions  are  scarcely  appreciable.  As  a  fact, 
we  can  easily  show  the  magnetic  effect  of  the  current 


THE  CONCEPTS  OF  ELECTROSTATICS.  135 

of  discharge  of  an  influence-machine  on  the  galvano- 
scope  although  we  could  hardly  have  made  the  orig- 
inal discovery  of  the  magnetic  effects  with  this  cur- 
rent. The  statical  distant  action  of  the  wire  poles  of 
a  galvanic  element  also  would  hardly  have  been  no- 
ticed had  not  the  phenomenon  been  known  from  a 
different  quarter  in  a  striking  form. 

If  we  wished  to  characterise  the  two  fields  in  their 
chief  and  most  general  features,  we  should  say  that  in 
the  first,  high  potentials  and  small  quantities  come 
into  play,  in  the  second  small  potentials  and  large 
quantities.  A  jar  which  is  discharging  and  a  galvanic 
element  deport  themselves  somewhat  like  an  air-gun 
and  the  bellows  of  an  organ.  The  first  gives  forth 
suddenly  under  a  very  high  pressure  a  small  quantity 
of  air ;  the  latter  liberates  gradually  under  a  very  slight 
pressure  a  large  quantity  of  air. 

In  point  of  principle,  too,  nothing  prevents  our  re- 
taining the  electrostatical  units  in  the  domain  of  gal- 
vanic electricity  and  in  measuring,  for  example,  the 
strength  of  a  current  by  the  number  of  electrostatic 
units  which  flow  per  second  through  its  cross-section. 
But  this  would  be  in  a  double  aspect  impractical.  In 
the  first  place,  we  should  totally  neglect  the  magnetic 
facilities  for  measurement  so  conveniently  offered  by 
the  current,  and  substitute  for  this  easy  means  a  method 
which  can  be  applied  only  with  difficulty  and  is  not 
capable  of  great  exactness.  In  the  second  place  our 
units  would  be  much  too  small,  and  we  should  find 


136          THE  CONCEPTS  OF  ELECTROSTATICS. 

ourselves  in  the  predicament  of  the  astronomer  who 
attempted  to  measure  celestial  distances  in  metres  in- 
stead of  in  radii  of  the  earth  and  the  earth's  orbit ;  for 
the  current  which  by  the  magnetic  C.  G.  S.  standard 
represents  the  unit,  would  require  a  flow  of  some 
30,000,000,000  electrostatic  units  per  second  through 
its  cross-section.  Accordingly,  different  units  must 
be  adopted  here.  The  development  of  this  point,  how- 
ever, lies  beyond  my  present  task. 


ON    THE    PRINCIPLE    OF    THE    CON- 
SERVATION OF  ENERGY.* 


IN  a  popular  lecture,  distinguished  for  its  charming 
simplicity  and  clearness,  which  Joule  delivered  in 
the  year  1847,!  that  famous  physicist  declares  that  the 
living  force  which  a  heavy  body  has  acquired  by  its 
descent  through  a  certain  height  and  which  it  carries 
with  it  in  the  form  of  the  velocity  with  which  it  is  im- 
pressed, is  the  equivalent  of  the  attraction  of  gravity 
through  the  space  fallen  through,  and  that  it  would  be 
"  absurd  "  to  assume  that  this  living  force  could  be  de- 
stroyed without  some  restitution  of  that  equivalent. 
He  then  adds:  "You  will  therefore  be  surprised  to 
hear  that  until  very  recently  the  universal  opinion  has 
been  that  living  force  could  be  absolutely  and  irre- 
vocably destroyed  at  any  one's  option."  Let  us  add 
that  to-day,  after  forty-seven  j'ears,  the  law  of  the  con- 
servation of  energy,  wherever  civilisation  exists,  is  ac- 

*  Published  in  Vol.  5,  No.  I,  of  The  Monist,  October,  1894,  being  in  part 
are-elaboration  of  the  treatise  Ueber  die  Erhaltung  der  Arbeit,  Prague.  1872. 

t  On  Matter,  Living  Farce,  and  Heat,  Joule :  Scientific  Papers,  London, 
1884,  I,  p.  265. 


138  ON"  THE  CONSERVATION  OF  ENERGY, 

cepted  as  a  fully  established  truth  and  receives  the 
widest  applications  in  all  domains  of  natural  science. 

The  fate  of  all  momentous  discoveries  is  similar. 
On  their  first  appearance  they  are  regarded  by  the 
majority  of  men  as  errors.  J.  R.  Mayer's  work  on  the 
principle  of  energy  (1842)  was  rejected  by  the  first 
physical  journal  of  Germany ;  Helmholtz's  treatise 
(1847)  met  with  no  better  success  ;  and  even  Joule,  to 
judge  from  an  intimation  of  Playfair,  seems  to  have 
encountered  difficulties  with  his  first  publication  (i  843). 
Gradually,  however,  people  are  led  to  see  that  the  new 
view  was  long  prepared  for  and  ready  for  enunciation, 
only  that  a  few  favored  minds  had  perceived  it  much 
earlier  than  the  rest,  and  in  this  way  the  opposition  of 
the  majority  is  overcome.  With  proofs  of  the  fruit- 
fulness  of  the  new  view,  with  its  success,  confidence 
in  it  increases.  The  majority  of  the  men  who  employ 
it  cannot  enter  into  a  deep-going  analysis  of  it ;  for 
them,  its  success  is  its  proof.  It  can  thus  happen  that 
a  view  which  has  led  to  the  greatest  discoveries,  like 
Black's  theory  of  caloric,  in  a  subsequent  period  in  a 
province  where  it  does  not  apply  may  actually  become 
an  obstacle  to  progress  by  its  blinding  our  eyes  to  facts 
which  do  not  fit  in  with  our  favorite  conceptions.  If 
a  theory  is  to  be  protected  from  this  dubious  role,  the 
grounds  and  motives  of  its  evolution  and  existence 
must  be  examined  from  time  to  time  with  the  utmost 
care. 

The  most  multifarious  physical  changes,  thermal, 


ON  THE  CONSERVATION  OF  ENERGY.  139 

electrical,  chemical,  and  so  forth,  can  be  brought 
about  by  mechanical  work.  When  such  alterations 
are  reversed  they  yield  anew  the  mechanical  work  in 
exactly  the  quantity  which  was  required  for  the  pro- 
duction of  the  part  reversed.  This  is  the  principle  of 
the  conservation  of  energy;  "energy  "  being  the  term 
which  has  gradually  come  into  use  for  that  "  inde- 
structible something  "  of  which  the  measure  is  me- 
chanical work. 

How  did  we  acquire  this  idea?  What  are  the 
sources  from  which  we  have  drawn  it  ?  This  question 
is  not  only  of  interest  in  itself,  but  also  for  the  impor- 
tant reason  above  touched  upon.  The  opinions  which 
are  held  concerning  the  foundations  of  the  law  of  en- 
ergy still  diverge  very  widely  from  one  another.  Many 
trace  the  principle  to  the  impossibility  of  a  perpetual 
motion,  which  they  regard  either  as  sufficiently  proved 
by  experience,  or  as  self-evident.  In  the  province  of 
pure  mechanics  the  impossibility  of  a  perpetual  mo- 
tion, or  the  continuous  production  of  -work  without 
some  permanent  alteration,  is  easily  demonstrated.  Ac- 
cordingly, if  we  start  from  the  theory  that  all  physical 
processes  are  purely  mechanical  processes,  motions  of 
molecules  and  atoms,  we  embrace  also,  by  this  me- 
chanical conception  of  physics,  the  impossibility  of  a 
perpetual  motion  in  the  whole  physical  domain.  At 
present  this  view  probably  counts  the  most  adherents. 
Other  inquirers,  however,  are  for  accepting  only  a 
purely  experimental  establishment  of  the  law  of  energy. 


140          ON  THE  CONSERVATION  OF  ENERGY. 

It  will  appear,  from  the  discussion  to  follow,  that 
all  the  factors  mentioned  have  co-operated  in  the  de- 
velopment of  the  view  in  question  ;  but  that  in  addi- 
tion to  them  a  logical  and  purely  formal  factor,  hitherto 
little  considered,  has  also  played  a  very  important  part. 

I.    THE   PRINCIPLE  OF  THE  EXCLUDED   PERPETUAL 
MOTION. 

The  law  of  energy  in  its  modern  form  is  not  iden- 
tical with  the  principle  of  the  excluded  perpetual  mo- 
tion, but  it  is  very  closely 
related  to  it.  The  latter 
principle,  however,  is  by 
no  means  new,  for  in  the 
province  of  mechanics  it 
has  controlled  for  centu- 
ries the  thoughts  and  in- 
vestigations of  the  great- 
Fie-4i-  est  thinkers.  Let  us  con- 

vince ourselves  of  this  by  the  study  of  a  few  historical 
examples. 

S.  Stevinus,  in  his  famous  work  Hypomnemata  ma- 
thematica,  Tom.  IV,  De  statica,  (Leyden,  1605,  p.  34), 
treats  of  the  equilibrium  of  bodies  on  inclined  planes. 
Over  a  triangular  prism  ABC,  one  side  of  which, 
A  C,  is  horizontal,  an  endless  cord  or  chain  is  slung, 
to  which  at  equal  distances  apart  fourteen  balls  of 
equal  weight  are  attached,  as  represented  in  cross- 
section  in  Figure  41.  Since  we  can  imagine  the  lower 


ON  THE  CONSERVATION  OF  ENERGY.          141 

symmetrical  part  of  the  cord  ABC  taken  away,  Stevinus 
concludes  that  the  four  balls  on  A  B  hold  in  equilib- 
rium the  two  balls  on  B  C.  For  if  the  equilibrium  were 
for  a  moment  disturbed,  it  could  never  subsist :  the 
cord  would  keep  moving  round  forever  in  the  same  di- 
rection,— we  should  have  a  perpetual  motion.  He  says: 

"But  if  this  took  place,  our  row  or  ring  of  balls  would  come 
once  more  into  their  original  position,  and  from  the  same  cause  the 
eight  globes  to  the  left  would  again  be  heavier  than  the  six  to  the 
right,  and  therefore  those  eight  would  sink  a  second  time  and  these 
six  rise,  and  all  the  globes  would  keep  up,  of  themselves,  a  continu- 
ous and  unending  motion,  -which  is  false."  * 

Stevinus,  now,  easily  derives  from  this  principle 
the  laws  of  equilibrium  on  the  inclined  plane  and  nu- 
merous other  fruitful  consequences. 

In  the  chapter  "Hydrostatics"  of 
the  same  work,  page  114,  Stevinus  sets 
up  the  following  principle  :   "Aquam 
datam,  datum  sibi  intra  aquam  locum 
servare," — a  given  mass  of  water  pre- 
serves within  water  its  given  place.  Fig.  42. 
This  principle  is  demonstrated  as  follows  (see  Fig. 
42): 

"  For,  assuming  it  to  be  possible  by  natural  means,  let  us  sup- 
pose that  A  does  not  preserve  the  place  assigned  to  it,  but  sinks 
down  to  D.  This  being  posited,  the  water  which  succeeds  A  will, 

*"Atqui  hoc  si  sit,  globorum  series  sive  corona  eundem  situm  cum  priore 
habebit,  eademque  de  causa  octo  globi  sinistri  ponderosiores  erunt  sex  dextris, 
ideoque  rursus  octo  illi  descendent,  sex  illi  ascendent,  istique  globi  ex  sese 
continuum  et  aeternum  motum  efficient,  quod  est/alsum." 


I42  ON  THE  CONSERVATION  OF  ENERGY. 

for  the  same  reason,  also  flow  down  to  D  ;  A  will  be  forced  out  of 
its  place  in  D  ;  and  thus  this  body  of  water,  for  the  conditions  in  it 
are  everywhere  the  same,  will  set  up  a  perpetual  motion,  which  is 
absurd. ' '  * 

From  this  all  the  principles  of  hydrostatics  are  de- 
duced. On  this  occasion  Stevinus  also  first  develops 
the  thought  so  fruitful  for  modern  analytical  mechanics 
that  the  equilibrium  of  a  system  is  not  destroyed  by 
the  addition  of  rigid  connexions.  As  we  know,  the 
principle  of  the  conservation  of  the  centre  of  gravity 
is  now  sometimes  deduced  from  D'Alembert's  princi- 
ple with  the  help  of  that  remark.  If  we  were  to  repro- 
duce Stevinus's  demonstration  to-day,  we  should  have 
to  change  it  slightly.  We  find  no  difficulty  in  imagin- 
ing the  cord  on  the  prism  possessed  of  unending  uni- 
form motion  if  all  hindrances  are  thought  away,  but 
we  should  protest  against  the  assumption  of  an  accel- 
erated motion  or  even  against  that  of  a  uniform  mo- 
tion, if  the  resistances  were  not  removed.  Moreover, 
for  greater  precision  of  proof,  the  string  of  balls  might 
be  replaced  by  a  heavy  homogeneous  cord  of  infinite 
flexibility.  But  all  this  does  not  affect  in  the  least  the 
historical  value  of  Stevinus's  thoughts.  It  is  a  fact, 
Stevinus  deduces  apparently  much  simpler  truths  from 
the  principle  of  an  impossible  perpetual  motion. 

*  "A  igitur,  (si  ullo  modo  per  naturam  fieri  possit)  locum  sibi  tributum 
non  servato,  ac  delabatur  in  D ;  quibus  positis  aqua  quae  ipsi  A  succedit  ean- 
dem  ob  causam  deffluet  in  D,  eademqne  ab  alia  istinc  expelletur,  atque  adeo 
aqua  haec  (cum  ubique  eadem  ratio  sit)  motunt  instituet  perpetuum,  qvod  ab- 
surdumftierit. ' ' 


ON  THE  CONSERVATION  OF  ENERGY.          143 

In  the  process  of  thought  which  conducted  Galileo 
to  his  discoveries  at  the  end  of  the  sixteenth  century, 
the  following  principle  plays  an  important  part,  that 
a  body  in  virtue  of  the  velocity  acquired  in  its  descent 
can  rise  exactly  as  high  as  it  fell.  This  principle, 
which  appears  frequently  and  with  much  clearness  in 
Galileo's  thought,  is  simply  another  form  of  the  prin- 
ciple of  excluded  perpetual  motion,  as  we  shall  see  it 
is  also  in  Huygens. 

Galileo,  as  we  know,  arrived  at  the  law  of  uniformly 
accelerated  motion  by  a  priori  considerations,  as  that 
law  which  was  the  "  simplest  and  most  natural,"  after 
having  first  assumed  a  different  law  which  he  was  com- 
pelled to  reject.  To  verify  his  law  he  executed  expe- 
riments with  falling  bodies  on  inclined  planes,  meas- 
uring the  times  of  descent  by  the  weights  of  the  water 
which  flowed  out  of  a  small  orifice  in  a  large  vessel. 
In  this  experiment  he  assumes  as  a  fundamental  prin- 
ciple, that  the  velocity  acquired  in  descent  down  an 
inclined  plane  always  corresponds  to  the  vertical  height 
descended  through,  a  conclusion  which  for  him  is  the 
immediate  outcome  of  the  fact  that  a  body  which  has 
fallen  down  one  inclined  plane  can,  with  the  velocity  it 
has  acquired,  rise  on  another  plane  of  any  inclination 
only  to  the  same  vertical  height.  This  principle  of 
the  height  of  ascent  also  led  him,  as  it  seems,  to  the 
law  of  inertia.  Let  us  hear  his  own  masterful  words 
in  the  Dialogo  terzo  (Opere,  Padova,  1744,  Tom.  III). 
On  page  96  we  read  : 


i44          ON  THE  CONSERVATION  OF  ENERGY. 

' '  I  take  it  for  granted  that  the  velocities  acquired  by  a  body 
in  descent  down  planes  of  different  inclinations  are  equal  if  the 
heights  of  those  planes  are  equal."* 

Then  he  makes  Salviati  say  in  the  dialogue  :f 

' '  What  you  say  seems  very  probable,  but  I  wish  to  go  further 
and  by  an  experiment  so  to  increase  the  probability  of  it  that  it  shall 

*  "Accipio,  gradus  velocitatis  ejusdem  mobilis  super  diversas  planorum 
inclinationes  acquisitos  tune  esse  aequales,  cum  corundum  planorum  eleva- 
tiones  aequales  sint." 

t  "  Voi  molto  probabilmente  discorrete,  ma  oltre  al  veri  simile  voglio  con 
una  esperienza  crescer  tanto  la  probability,  che  poco  gli  manchi  all'aggua- 
gliarsi  ad  una  ben  necessaria  dimostrazione.  Figuratevi  questo  foglio  essere 
una  parete  eretta  al  orizzonte,  e  da  un  chiodo  fitto  in  essa  pendere  una  palla 
di  piombo  d'un'oncia,  o  due,  sospesa  dal  sottil  filo  A  B  )ungo  due,  o  tre  braccia 
perpendicolare  all'  orrizonte,  e  nella  parete  segnate  una  linea  orrizontale  DC 
segante  a  squadra  il  perpendicolo  AB,  il  quale  sia  lontano  dalla  parete  due 
dita  in  circa,  trasferendo  poi  il  filo  A  B  colla  palla  in  A  C,  lasciata  essa  palla  in 
liberta,  la  quale  primier  amente  vedrete  scendere  descrivendo  1'arco  CB  D,  e 
di  tanto  trapassare  il  termine  B,  che  scorrendo  per  1'arco  B  D  sormontera  fino 
quasi  alia  segnata  parallela  CD,  restando  di  per  vernirvi  per  piccolissimo  in- 
tervallo,  toltogli  il  precisamente  arrivarvi  dall'  impedimento  dell'aria,  e  del 
filo.  Dal  che  possiamo  veracemente  concludere,  che  1'impeto  acquistato  nel 
punto  B  dalla  palla  nello  scendere  per  1'arco  CB,  fu  tanto,  che  bastd  a  riso- 
spingersi  per  un  simile  arco  B  D  alia  medesima  altezza  ;  iatta.  e  piu  volte  re- 
iterata  cotale  esperienza,  voglio,  che  fiechiamo  nella  parete  rasente  al  per- 
pendicolo A  B  un  chiodo  come  in  E,  owero  in  F,  che  sporga  in  fuori  cinque,  o 
sei  dita,  e  questo  acciocchfe  il  filo  A  Ctornando  come  prima  a  riportar  la  palla 
Cper  1'arco  C  B,  giunta  che  ella  sia  in  B,  inoppando  il  filo  nel  chiodo  E,  sia 
costretta  a  camminare  per  la  circonferenza  B  G  descritta  in  torno  al  centre  E, 
dal  che  vedremo  quello,  che  potra  far  quel  medesimo  impeto,  che  dianzi  con- 
cepizo  nel  medesimo  termine  B,  sospinse  Vistesso  mobile  per  1'arco  E  D  all'al- 
tezza  dell'orizzonale  CD.  Ora,  Signori,  voi  vedrete  con  gusto  condursi  la 
palla  all'orizzontale  nel  punto  G,  e  1'istesso  accadere,  1'intoppo  si  metesse 
piu  basso,  come  in  F,  dove  la  palla  descriverebbe  1'arco  B  y,  terminando  sem- 
pre  la  sua  salita  precisamente  nella  linea  CD,  e  quando  1'intoppe  del  chiodo 
fusse  tanto  basso,  che  1'avanzo  del  filo  sotto  di  lui  non  arivasse  all'altezza  di 
CD  (il  che  accaderebbe,  quando  fusse  pia  vicino  all  punto  B,  che  al  sega- 
mento  dell'  A  B  coll'orizzontale  CD),  allora  il  filo  cavalcherebbe  il  chiodo,  e 
segli  avolgerebbe  intorno.  Questa  esperienza  non  lascia  luogo  di  dubitare 
della  verita  del  supposto  :  imperocchfc  essendo  li  due  archi  CB,  DB  equal!  e 
similmento  posti,  1'acquisto  di  momento  fatto  per  la  scesa  nell'arco  CB,  e  il 
medesimo,  che  il  fatto  per  la  scesa  deU'arco  DB;  ma  il  momento  acquistato 
in  B  per  1'arco  CB  k  potente  a  risospingere  in  su  il  medesimo  mobile  per  1'arco 
BD;  adunque  anco  il  momento  acquistato  nella  scesa  D  B  it  eguale  a  quello, 
che  sospigne  1'istesso  mobile  pel  medesimo  arco  da  B  in  D,  sicche  universal- 


ON  THE  CONSERVATION  OF  ENERGY. 


amount  almost  to  absolute  demonstration.  Suppose  this  sheet  of 
paper  to  be  a  vertical  wall,  and  from  a  nail  driven  in  it  a  ball  of  lead 
weighing  two  or  three  ounces  to  hang  by  a  very  fine  thread  AB  four 
or  five  feet  long.  (Fig.  43.)  On  the  wall  mark  a  horizontal  line  DC 
perpendicular  to  the  vertical  ABt  which  latter  ought  to  hang  about 
two  inches  from  the  wall.  If  now  the  thread  AB  with  the  ball 
attached  take  the  position  AC  and  the  ball  be  let  go,  you  will  see 
the  ball  first  descend  through  the  arc  CB  and  passing  beyond 
B  rise  through  the  arc 
BD  almost  to  the  level 
of  the  line  CD,  being 
prevented  from  reach- 
ing it  exactly  by  the  re- 
sistance of  the  air  and 
of  the  thread.  From 
this  we  may  truly  con- 
clude that  its  impetus  at 
the  point  B,  acquired  by 
its  descent  through  the 
arc  CB,  is  sufficient  to 
urge  it  through  a  similar  arc  BD  to  the  same  height.  Having 
performed  this  experiment  and  repeated  it  several  times,  let  us 
drive  in  the  wail,  in  the  projection  of  the  vertical  AB,  as  at  E  or 
at  F,  a  nail  five  or  six  inches  long,  so  that  the  thread  AC,  carrying 
as  before  the  ball  through  the  arc  CB,  at  the  moment  it  reaches 
the  position  AB,  shall  strike  the  nail  E,  and  the  ball  be  thus  com- 
pelled to  move  up  the  arc  BG  described  about  E  as  centre. 
Then  we  shall  see  what  the  same  impetus  will  here  accomplish, 
acquired  now  as  before  at  the  same  point  B,  which  then  drove  the 

mente  ogni  memento  acquistato  per  la  scesa  dun  arco  e  eguale  a  quello,  che 
pud  far  risalire  1'istesso  mobile  pel  medesimo  arco  :  ma  i  momenti  tutti  che 
fanno  resalire  per  tutti  gli  archi  B  D,  BG,  By  sono  eguali,  poiche  son  fatti 
dal  istesso  medesimo  momer.to  acquistato  per  la  scesa  CB,  come  mostra 
1'esperienza :  adunque  tutti  i  momenti,  che  si  acquistano  per  le  scese  negli 
archi  D  B,  GB.  J  B  sono  eguali." 


146  ON  THE  CONSERVATION  OF  ENERGY, 

same  moving  body  through  the  arc  BD  to  the  height  of  the  hori- 
zontal CD.  Now  gentlemen,  you  will  be  pleased  to  see  the  ball 
rise  to  the  horizontal  line  at  the  point  G,  and  the  same  thing  also 
happen  if  the  nail  be  placed  lower  as  at  Ft  in  which  case  the  ball 
would  describe  the  arc  BJ,  always  terminating  its  ascent  precisely 
at  the  line  CD.  If  the  nail  be  placed  so  low  that  the  length  of 
thread  below  it  does  not  reach  to  the  height  of  CD  (which  would 
happen  if  F  were  nearer  B  than  to  the  intersection  of  AB  with  the 
horizontal  CD),  then  the  thread  will  wind  itself  about  the  nail. 
This  experiment  leaves  no  room  for  doubt  as  to  the  truth  of  the 
supposition.  For  as  the  two  arcs  CB,  DB  are  equal  and  similarly 
situated,  the  momentum  acquired  in  the  descent  of  the  arc  CB  is 
the  same  as  that  acquired  in  the  descent  of  the  arc  DB  ;  but  the 
momentum  acquired  at  B  by  the  descent  through  the  arc  CB  is  cap- 
able of  driving  up  the  same  moving  body  through  the  arc  BD; 
hence  also  the  momentum  acquired  in  the  descent  DB  is  equal  to 
that  which  drives  the  same  moving  body  through  the  same  arc 
from  B  to  D,  so  that  in  general  every  momentum  acquired  in  the 
descent  of  an  arc  is  equal  to  that  which  causes  the  same  moving 
body  to  ascend  through  the  same  arc  ;  but  all  the  momenta  which 
cause  the  ascent  of  all  the  arcs  BD,  BG,  BJ,  are  equal  since  they 
are  made  by  the  same  momentum  acquired  in  the  descent  CB,  as 
the  experiment  shows  :  therefore  all  the  momenta  acquired  in  the 
descent  of  the  arcs  DB,  GB,  JB  are  equal." 

The  remark  relative  to  the  pendulum  may  be  ap- 
plied to  the  inclined  plane  and  leads  to  the  law  of  in- 
ertia. We  read  on  page  124  :* 

*"  Constat  jam,  quod  mobile  ex  quiete  in  A  descendens  per  A  B,  gradus 
acquirit  velocitatis  juxta  temporis  ipsius  incrementum  :  gradum  vero  in  B 
esse  maximum  acquisitorum,  et  suapte  natura  immutabiliter  impressum,  sub- 
latis  scilicet  causis  acceleration!1?  novae,  aut  retardationis  :  accelerationis  in- 
quam,  si  adhuc  super  extenso  piano  ulterius  progrederetur ;  retardationis 
vero,  dum  super  planum  acclive  B  C  fit  reflexio :  in  horizontali  autem  G  H 
aequabilis  motus  juxta  gradum  velocitatis  ex  A  in  B  acquisitae  in  infinitum 
extenderetur. 


ON  THE  CONSERVATION  OF  ENERGY.  I47 

"It  is  plain  now  that  a  movable  body,  starting  from  rest  at  A 
and  descending  down  the  inclined  plane  A  B,  acquires  a  velocity 
proportional  to  the  increment  of  its  time :  the  velocity  possessed 
at  B  is  the  greatest  of  the  velocities  acquired,  and  by  its  nature 
immutably  impressed,  provided  all  causes  of  new  acceleration  or 
retardation  are  taken  away  :  I  say  acceleration,  having  in  view  its 
possible  further  progress  along  the  plane  extended  ;  retardation,  in 
view  of  the  possibility  of  its  being  reversed  and  made  to  mount  the 
ascending  plane  B  C.  But  in  the  horizontal  plane  C II  its  equable 
motion,  according  to  its  velocity  as  acquired  in  the  descent  from  A 
to  £,  will  be  continued  ad  inf. nitum. "  (Fig.  44.) 

Huygens,  upon  whose  shoulders  the  mantel  of  Gali- 
leo fell,  forms  a  sharper  conception  of  the  law  of  inertia 


B 

Fig.  44- 

and  generalises  the  principle  respecting  the  heights  of 
ascent  which  was  so  fruitful  in  Galileo's  hands.  He 
employs  the  latter  principle  in  the  solution  of  the  prob- 
lem of  the  centre  of  oscillation  and  is  perfectly  clear  in 
the  statement  that  the  principle  respecting  the  heights 
of  ascent  is  identical  with  the  principle  of  the  excluded 
perpetual  motion. 

The  following  important  passages  then  occur  (Hu- 
genii,  Horologium  oscillatorium,  pars  secunda).  Hy- 
potheses: 

1 '  If  gravity  did  not  exist,  nor  the  atmosphere  obstruct  the  mo- 


148          ON  THE  CONSERVATION  OF  ENERGY. 

tions  of  bodies,  a  body  would  keep  up  forever  the  motion  once  im- 
pressed upon  it,  with  equable  velocity,  in  a  straight  line. ' '  * 

In  part  four  of  the  Horologium  de  centra  oscillationis 
we  read : 

1 '  If  any  number  of  weights  be  set  in  motion  by  the  force  of 
gravity,  the  common  centre  of  gravity  of  the  weights  as  a  whole 
cannot  possibly  rise  higher  than  the  place  which  it  occupied  when 
the  motion  began. 

"That  this  hypothesis  of  ours  may  arouse  no  scruples,  we 
will  state  that  it  simply  imports,  what  no  one  has  ever  denied,  that 
heavy  bodies  do  not  move  upwards. — And  truly  if  the  devisers  of 
the  new  machines  who  make  such  futile  attempts  to  construct  a 
perpetual  motion  would  acquaint  themselves  with  this  principle, 
they  could  easily  be  brought  to  see  their  errors  and  to  understand 
that  the  thing  is  utterly  impossible  by  mechanical  means,  "f 

There  is  possibly  a  Jesuitical  mental  reservation 
contained  in  the  words  "mechanical  means."  One 
might  be  led  to  believe  from  them  that  Huygens  held 
a  non-mechanical  perpetual  motion  for  possible. 

The  generalisation  of  Galileo's  principle  is  still 
more  clearly  put  in  Prop.  IV  of  the  same  chapter  : 

"  If  a  pendulum,  composed  of  several  weights,  set  in  motion 
from  rest,  complete  any  part  of  its  full  oscillation,  and  from  that 

*  "  Si  gravitas  non  esset,  neque  a6r  motui  corporum  officeret,  unumquod- 
que  eorum,  acceptum  semel  motum  continuaturum  velocitate  aequabili,  se- 
cundum  lineam  rectam." 

t "  Si  pond'era  quotlibet,  vi  gravitatis  suae,  moveri  incipiant ;  non  posse 
centrum  gravitatis  ex  ipsis  compositae  altius,  quam  ubi  incipiente  motu  repe- 
riebatur,  ascendere. 

"  Ipsa  vero  hypothesis  nostra  quominus  scrupulum  moveat,  nihil  aliud 
sibi  velle  ostendemus,  quam,  quod  nemo  unquam  negavit,  gravia  neinpe  sur- 
sum  non  ferri. — Et  sane,  si  hac  eadem  uti  scirent  novorum  operum  machina- 
tores,  qui  motum  perpetuum  irrito  conatu  moliuntur,  facile  suos  ipsi  errores 
deprehenderent,  intelligerentque  rem  earn  mechanica  ratione  baud  quaquam 
possibilem  esse." 


ON  THE  CONSERVATION  OF  ENERGY,          149 

point  onwards,  the  individual  weights,  with  their  common  connex- 
ions dissolved,  change  their  acquired  velocities  upwards  and  ascend 
as  far  as  they  can,  the  common  centre  of  gravity  of  all  will  be  car- 
ried up  to  the  same  altitude  with  that  which  it  occupied  before  the 
beginning  of  the  oscillation."* 

On  this  last  principle  now,  which  is  a  generalisa- 
tion, applied  to  a  system  of  masses,  of  one  of  Galileo's 
ideas  respecting  a  single  mass  and  which  from  Huy- 
gens's  explanation  we  recognise  as  the  principle  of  ex- 
cluded perpetual  motion,  Huygens  grounds  his  theory 
of  the  centre  of  oscillation.  Lagrange  characterises 
this  principle  as  precarious  and  is  rejoiced  at  James 
Bernoulli's  successful  attempt,  in  1681,  to  reduce  the 
theory  of  the  centre  of  oscillation  to  the  laws  of  the 
lever,  which  appeared  to  him  clearer.  All  the  great 
inquirers  of  the  seventeenth  and  eighteenth  centuries 
broke  a  lance  on  this  problem,  and  it  led  ultimately, 
in  conjunction  with  the  principle  of  virtual  velocities, 
to  the  principle  enunciated  by  D'Alembert  in  1743  in 
his  Traite  de  dynamique,  though  previously  employed 
in  a  somewhat  different  form  by  Euler  and  Hermann. 

Furthermore,  the  Huygenian  principle  respecting 
the  heights  of  ascent  became  the  foundation  of  the 
"law  of  the  conservation  of  living  force,"  as  that  was 
enunciated  by  John  and  Daniel  Bernoulli  and  em- 

*  "  Si  pendulum  e  pluribus  ponderibus  compositum,  atque  e  quiete  dimis- 
sum,  partem  quamcunque  oscillationis  integrae  confecerit,  atque  inde  porro 
intelligantur  pondera  ejus  singula,  relicto  communi  vinculo,  celeritates  acqui- 
sitas  sursum  convertere,  ac  quousque  possunt  ascendere  ;  hoc  facto  centrum 
gravitatis  ex  omnibus  compositae,  ad  eandem  altitudinem  reversuni  erit,  quam 
ante  inceptam  oscillationem  obtinebat." 


150  ON  THE  CONSERVATION  OF  ENERGY. 

ployed  with  such  signal  success  by  the  latter  in  his 
Hydrodynamics.  The  theorems  of  the  Bernoullis  differ 
in  form  only  from  Lagrange's  expression  in  the  Ana- 
lytical Mechanics. 

The  manner  in  which  Torricelli  reached  his  famous 
law  of  efflux  for  liquids  leads  again  to  our  principle. 
Torricelli  assumed  that  the  liquid  which  flows  out  of 
the  basal  orifice  of  a  vessel  cannot  by  its  velocity  of 
efflux  ascend  to  a  greater  height  than  its  level  in  the 
vessel. 

Let  us  next  consider  a  point  which  belongs  to  pure 
mechanics,  the  history  of  the  principle  of  virtual  mo- 
tions or  virtual  velocities.  This  principle  was  not  first 
enunciated,  as  is  usually  stated,  and  as  Lagrange  also 
asserts,  by  Galileo,  but  earlier,  by  Stevinus.  In  his 
Trochleostatica  of  the  above- cited  work,  page  72,  he 
says : 

"  Observe  that  this  axiom  of  statics  holds  good  here  : 

"As  the  space  of  the  body  acting  is  to  the  space  of  the  body 
acted  upon,  so  is  the  power  of  the  body  acted  upon  to  the  power  of 
the  body  acting."* 

Galileo,  as  we  know,  recognised  the  truth  of  the 
principle  in  the  consideration  of  the  simple  machines, 
and  also  deduced  the  laws  of  the  equilibrium  of  liquids 
from  it. 

Torricelli  carries  the  principle  back  to  the  proper- 
ties of  the  centre  of  gravity.  The  condition  control- 

*  "  Notato  autem  hie  illud  staticum  axioma  etiam  locum  habere  : 
"  Ut  spatium  agentis  ad  spatium  patientis 
Sic  potentia  patientis  ad  potentiam  agentis." 


ON  THE  CONSERVATION  OF  ENERGY.  151 

ling  equilibrium  in  a  simple  machine,  in  which  power 
and  load  are  represented  by  weights,  is  that  the  com- 
mon centre  of  gravity  of  the  weights  shall  not  sink. 
Conversely,  if  the  centre  of  gravity  cannot  sink  equi- 
librium obtains,  because  heavy  bodies  of  themselves 
do  not  move  upwards.  In  this  form  the  principle  of 
virtual  velocities  is  identical  with  Huygens's  principle 
of  the  impossibility  of  a  perpetual  motion. 

John  Bernoulli,  in  1717,  first  perceived  the  universal 
import  of  the  principle  of  virtual  movements  for  all 
systems ;  a  discovery  stated  in  a  letter  to  Varignon. 
Finally,  Lagrange  gives  a  general  demonstration  of 
the  principle  and  founds  upon  it  his  whole  Analytical 
Mechanics.  But  this  general  demonstration  is  based 
after  all  upon  Huygens  and  Torricelli's  remarks.  La- 
grange,  as  is  known,  conceives  simple  pulleys  arranged 
in  the  directions  of  the  forces  of  the  system,  passes  a 
cord  through  these  pulleys,  and  appends  to  its  free 
extremity  a  weight  which  is  a  common  measure  of  all 
the  forces  of  the  system.  With  no  difficulty,  now,  the 
number  of  elements  of  each  pulley  may  be  so  chosen 
that  the  forces  in  question  shall  be  replaced  by  them. 
It  is  then  clear  that  if  the  weight  at  the  extremity  can- 
not sink,  equilibrium  subsists,  because  heavy  bodies 
cannot  of  themselves  move  upwards.  If  we  do  not  go 
so  far,  but  wish  to  abide  by  Torricelli's  idea,  we  may 
conceive  every  individual  force  of  the  system  replaced 
by  a  special  weight  suspended  from  a  cord  passing 
over  a  pulley  in  the  direction  of  the  force  and  attached 


i52  ON  THE  CONSERVATION  OF  ENERGY, 

at  its  point  of  application.  Equilibrium  subsists  then 
when  the  common  centre  of  gravity  of  all  the  weights 
together  cannot  sink.  The  fundamental  supposition 
of  this  demonstration  is  plainly  the  impossibility  of  a 
perpetual  motion. 

Lagrange  tried  in  every  way  to  supply  a  proof  free 
from  extraneous  elements  and  fully  satisfactory,  but 
without  complete  success.  Nor  were  his  successors 
more  fortunate. 

The  whole  of  mechanics,  thus,  is  based  upon  an 
idea,  which,  though  unequivocal,  is  yet  unwonted  and 
not  coequal  with  the  other  principles  and  axioms  of 
mechanics.  Every  student  of  mechanics,  at  some  stage 
of  his  progress,  feels  the  uncomfortableness  of  this 
state  of  affairs ;  every  one  wishes  it  removed ;  but  sel- 
dom is  the  difficulty  stated  in  words.  Accordingly,  the 
zealous  pupil  of  the  science  is  highly  rejoiced  when  he 
reads  in  a  master  like  Poinsot  (Theorie  generate  de 
fequilibre  et  du  mouvement  des  systemes)  the  following 
passage,  in  which  that  author  is  giving  his  opinion  of 
the  Analytical  Mechanics : 

"  In  the  meantime,  because  our  attention  in  that  work  was  first 
wholly  engrossed  with  the  consideration  of  its  beautiful  develop- 
ment of  mechanics,  which  seemed  to  spring  complete  from  a  single 
formula,  we  naturally  believed  that  the  science  was  completed  or 
that  it  only  remained  to  seek  the  demonstration  of  the  principle  of 
virtual  velocities.  But  that  quest  brought  back  all  the  difficulties 
that  we  had  overcome  by  the  principle  itself.  That  law  so  general, 
wherein  are  mingled  the  vague  and  unfamiliar  ideas  of  infinitely 
small  movements  and  of  perturbations  of  equilibrium,  only  grew 


ON  THE  CONSERVATION  OF  ENERGY.          153 

obscure  upon  examination ;  and  the  work  of  Lagrange  supplying 
nothing  clearer  than  the  march  of  analysis,  we  saw  plainly  that  the 
clouds  had  only  appeared  lifted  from  the  course  of  mechanics  be- 
cause they  had,  so  to  speak,  been  gathered  at  the  very  origin  of  that 
science. 

"At  bottom,  a  general  demonstration  of  the  principle  of  virtual 
velocities  would  be  equivalent  to  the  establishment  of  the  whole 
of  mechanics  upon  a  different  basis  :  for  the  demonstration  of  a 
law  which  embraces  a  whole  science  is  neither  more  nor  less  than 
the  reduction  of  that  science  to  another  law  just  as  general,  but 
evident,  or  at  least  more  simple  than  the  first,  and  which,  conse- 
quently, would  render  that  useless."  * 

According  to  Poinsot,  therefore,  a  proof  of  the 
principle  of  virtual  movements  is  tantamount  to  a  to- 
tal rehabilitation  of  mechanics. 

Another  circumstance  of  discomfort  to  the  mathe- 
matician is,  that  in  the  historical  form  in  which  me- 
chanics at  present  exists,  dynamics  is  founded  on 
statics,  whereas  it  is  desirable  that  in  a  science  which 
pretends  to  deductive  completeness  the  more  special 

*"Cependant»  comme  dans  cet  ouvrage  on  ne  fut  d'abord  attentif  qu'a 
considerer  ce  beau  developpement  de  la  mccanique  qui  semblait  sortir  tout 
entire  d'une  seule  et  mfime  formula,  on  crut  naturellement  que  la  science  etait 
faite,  et  qu'il  ne  restait  plus  qu'a  chercher  la  demonstration  du  principe  des 
vitesses  virtuelles.  Mais  cette  recherche  ramena  toutes  les  difficulties  qu'on 
avail  franchies  par  le  principe  mfime.  Cette  loi  si  ge'ritfrale,  ou  se  m£lent  des 
id£es  vagues  et  6trangeres  de  mouvements  infinement  petits  et  de  perturbation 
d'e'quilibre,  ne  fit  en  quelque  sorte  que  s'obsurcir  &  1'examen  ;  et  le  livre  de 
Lagrange  n'offrant  plus  alors  rien  de  clair  que  la  marche  des  calculs,  on  vit 
bien  que  les  nuages  n'avaient  paru  leve'  sur  le  cours  de  la  me'canique  que 
parcequ'ils  e"taient,  pour  ainsi  dire,  rassembles  a  1'origine  mCme  de  cette 
science. 

"Une  demonstration  general e  du  principe  des  vitesses  virtuelles  devait 
au  fond  revenir  a  dtablir  le  mecanique  entifcre  sur  une  autre  base  :  car  la  de- 
monstration d'une  loi  qui  embrasse  toute  une  science  ne  peut  Ctre  autre  chose 
que  la  reduction  de  cette  science  .1  une  autre  loi  aussi  K<§ne"rale,  mais  eVidente, 
ou  du  moins  plus  simple  que  la  premiere,  et  qui  partant  la  rende  inutile." 


154  ON  THE  CONSERVATION  OF  ENERGY. 

statical  theorems  should  be  deducible  from  the  more 
general  dynamical  principles. 

In  fact,  a  great  master,  Gauss,  gave  expression  to 
this  desire  in  his  presentment  of  the  principle  of  least 
constraint  (Crelle's  Journal  fur  reine  und  angewandte 
Mathematik,  Vol.  IV,  p.  233)  in  the  following  words : 
"  Proper  as  it  is  that  in  the  gradual  development  of  a 
science,  and  in  the  instruction  of  individuals,  the  easy 
should  precede  the  difficult,  the  simple  the  complex, 
the  special  the  general,  yet  the  mind,  when  once  it  has 
reached  a  higher  point  of  view,  demands  the  contrary 
course,  in  which  all  statics  shall  appear  simply  as  a 
special  case  of  mechanics."  Gauss's  own  principle, 
now,  possesses  all  the  requisites  of  universality,  but 
its  difficulty  is  that  it  is  not  immediately  intelligible 
and  that  Gauss  deduced  it  with  the  help  of  D'Alem- 
bert's  principle,  a  procedure  which  left  matters  where 
they  were  before. 

Whence,  now,  is  derived  this  strange  part  which 
the  principle  of  virtual  motion  plays  in  mechanics  ? 
For  the  present  I  shall  only  make  this  reply.  It  would 
be  difficult  for  me  to  tell  the  difference  of  impression 
which  Lagrange's  proof  of  the  principle  made  on  me 
when  I  first  took  it  up  as  a  student  and  when  I  subse- 
quently resumed  it  after  having  made  historical  re- 
searches. It  first  appeared  to  me  insipid,  chiefly  on 
account  of  the  pulleys  and  the  cords  which  did  not  fit 
in  with  the  mathematical  view,  and  whose  action  I 
would  much  rather  have  discovered  from  the  principle 


ON  THE  CONSERVATION  OF  ENERGY.          155 

itself  than  have  taken  for  granted.  But  now  that  I 
have  studied  the  history  of  the  science  I  cannot  imag- 
ine a  more  beautiful  demonstration. 

In  fact,  through  all  mechanics  it  is  this  self-same 
principle  of  excluded  perpetual  motion  which  accom- 
plishes almost  all,  which  displeased  Lagrange,  but 
which  he  still  had  to  employ,  at  least  tacitly,  in  his  own 
demonstration.  If  we  give  this  principle  its  proper 
place  and  setting,  the  paradox  is  explained. 

The  principle  of  excluded  perpetual  motion  is  thus 
no  new  discovery ;  it  has  been  the  guiding  idea,  for 
three  hundred  years,  of  all  the  great  inquirers.  But 
the  principle  cannot  properly  be  based  upon  mechani- 
cal perceptions.  For  long  before  the  development  of 
mechanics  the  conviction  of  its  truth  existed  and  even 
contributed  to  that  development.  Its  power  of  con- 
viction, therefore,  must  have  more  universal  and 
deeper  roots.  We  shall  revert  to  this  point. 

II.  MECHANICAL  PHYSICS. 

It  cannot  be  denied  that  an  unmistakable  tendency 
has  prevailed,  from  Democritus  to  the  present  day,  to 
explain  all  physical  events  mechanically.  Not  to  men- 
tion earlier  obscure  expressions  of  that  tendency  we 
read  in  Huygens  the  following :  * 

"There  can  be  no  doubt  that  light  consists  of  the  motion  of  a 
certain  substance.  For  if  we  examine  its  production,  we  find  that 

*  Traiti  tie  la  ittntitrf,  Lcyden,  1690,  p.  a. 


156          ON  THE  CONSERVATION  OF  ENERGY, 

here  on  earth  it  is  principally  fire  and  flame  which  engender  it,  both 
of  which  contain  beyond  doubt  bodies  which  are  in  rapid  move- 
ment, since  they  dissolve  and  destroy  many  other  bodies  more  solid 
than  they  :  while  if  we  regard  its  effects,  we  see  that  when  light  is 
accumulated,  say  by  concave  mirrors,  it  has  the  property  of  com- 
bustion just  as  fire  has,  that  is  to  say,  it  disunites  the  parts  of 
bodies,  which  is  assuredly  a  proof  of  motion,  at  least  in  the  true 
philosophy,  in  which  the  causes  of  all  natural  effects  are  conceived 
as  mechanical  causes.  Which  in  my  judgment  must  be  accomplished 
or  all  hope  of  ever  understanding  physics  renounced."* 

S.  Carnot,f  in  introducing  the  principle  of  excluded 
perpetual  motion  into  the  theory  of  heat,  makes  the 
following  apology : 

"It  will  be  objected  here,  perhaps,  that  a  perpetual  motion 
proved  impossible  for  purely  mechanical  actions,  is  perhaps  not  so 
when  the  influence  of  heat  or  of  electricity  is  employed.  But  can 
phenomena  of  heat  or  electricity  be  thought  of  as  due  to  anything 
else  than  to  certain  motions  of  bodies,  and  as  such  must  they  not  be 
subject  to  the  general  laws  of  mechanics  ?  "  \ 

*L'on  ne  sgaurait  douter  que  la  lumiere  ne  consiste  dans  le  mouvement  de 
certaine  matiere.  Car  soil  qu'on  regarde  sa  production,  on  trouve  qu'i§y  sur 
la  terre  c'est  principalement  le  feu  et  la  flamme  qui  1'engendrent,  lesquels 
contient  sans  doute  des  corps  qui  sont  dans  un  mouvement  rapide,  puis  qu'ils 
dissolvent  et  fondent  plusieurs  autres  corps  des  plus  solides  :  soil  qu'on  re- 
garde  ses  effets,  on  voit  que  quand  la  lumiere  est  ramassee,  comme  par  des 
miroires  concaves,  elle  a  la  vertu  de  bruler  comme  le  feu.  c-est-a-dire  qu'elle 
desunit  les  parties  des  corps;  ce  qui  marque  assurement  du  mouvement,  au 
moins  dans  la  vraye  Philosophic,  dans  laquelle  on  conceit  la  cause  de  tous  les 
effets  naturels  par  des  raisons  de  mechanique.  Ce  qu'il  faut  faire  &.  mon  avis, 
ou  bien  renoncer  a  tout  espe'rance  de  jainais  rien  comprendre  dans  la  Phy- 
sique." 

t  Sur  la  puissance  motrice  dufeu.     (Paris,  1824.) 

J  "  On  objectra  peut-fitre  ici  que  le  mouvement  perpe'tuel,  demontre'  im- 
possible par  les  seules  actions  mecaniques,  ne  Test  peut-6tre  pas  lorsqu'on 
emploie  1'influence  soil  de  la  chaleur,  soil  de  I'e'lectricite  ;  mais  peut-on  con- 
cevoir  les  phenomenes  de  la  chaleur  et  de  1'electricite  comme  dus  &  autre 
chose  qu'Jl  des  mouvements  quelcon ques  des  corps  et  comme  tels  ne  doivent-ils 
pas  fitre  soumis  aux  lois  generales  de  la  mecanique  ?  " 


ON  THE  CONSERVATION  OF  ENERGY,          157 

These  examples,  which  might  be  multiplied  by 
quotations  from  recent  literature  indefinitely,  show 
that  a  tendency  to  explain  all  things  mechanically 
actually  exists.  This  tendency  is  also  intelligible. 
Mechanical  events  as  simple  motions  in  space  and 
time  best  admit  of  observation  and  pursuit  by  the  help 
of  our  highly  organised  senses.  We  reproduce  mechan  - 
ical  processes  almost  without  effort  in  our  imagina- 
tion. Pressure  as  a  circumstance  that  produces  mo- 
tion is  very  familiar  to  us  from  daily  experience.  All 
changes  which  the  individual  personally  produces  in 
his  environment,  or  humanity  brings  about  by  means 
of  the  arts  in  the  world,  are  effected  through  the  in- 
strumentality of  motions.  Almost  of  necessity,  there- 
fore, motion  appears  to  us  as  the  most  important 
physical  factor.  Moreover,  mechanical  properties  may 
be  discovered  in  all  physical  events.  The  sounding 
bell  trembles,  the  heated  body  expands,  the  electrified 
body  attracts  other  bodies.  Why,  therefore,  should 
we  not  attempt  to  grasp  all  events  under  their  mechan- 
ical aspect,  since  that  is  so  easily  apprehended  and 
most  accessible  to  observation  and  measurement?  In 
fact,  no  objection  is  to  be  made  to  the  attempt  to  elu- 
cidate the  properties  of  physical  events  by  mechanical 
analogies. 

But  modern  physics  has  proceeded  very  far  in  this 
direction.  The  point  of  view  which  Wundt  represents 
in  his  excellent  treatise  On  the  Physical  Axioms  is  prob- 


158  ON  THE  CONSERVATION  OF  ENERGY. 

ably  shared  by  the  majority  of  physicists.    The  axioms 
of  physics  which  Wundt  sets  up  are  as  follows  : 

1.  All  natural  causes  are  motional  causes. 

2.  Every  motional  cause  lies   outside   the  object 
moved. 

3.  All  motional  causes  act  in  the  direction  of  the 
straight  line  of  junction,  and  so  forth. 

4.  The  effect  of  every  cause  persists. 

5.  Every  effect  involves  an  equal  countereffect. 

6.  Every  effect  is  equivalent  to  its  cause. 

These  principles  might  be  studied  properly  enough 
as  fundamental  principles  of  mechanics.  But  when 
they  are  set  up  as  axioms  of  physics,  their  enunciation 
is  simply  tantamount  to  a  negation  of  all  events  ex- 
cept motion. 

According  to  Wundt,  all  changes  of  nature  are 
mere  changes  of  place.  All  causes  are  motional  causes 
(page  26).  Any  discussion  of  the  philosophical  grounds 
on  which  Wundt  supports  his  theory  would  lead  us 
deep  into  the  speculations  of  the  Eleatics  and  the 
Herbartians.  Change  of  place,  Wundt  holds,  is  the 
only  change  of  a  thing  in  which  a  thing  remains  iden- 
tical with  itself.  If  a  thing  changed  qualitatively,  we 
should  be  obliged  to  imagine  that  something  was  an- 
nihilated and  something  else  created  in  its  place,  which 
is  not  to  be  reconciled  with  our  idea  of  the  identity  of 
the  object  observed  and  of  the  indestructibility  of 
matter.  But  we  have  only  to  remember  that  the  Ele- 
atics encountered  difficulties  of  exactly  the  same  sort 


ON  THE  CONSERVATION  OF  ENERGY.          159 

in  motion.  Can  we  not  also  imagine  that  a  thing  is 
destroyed  in  one  place  and  in  another  an  exactly  simi- 
lar thing  created  ?  After  all,  do  we  really  know  more 
why  a  body  leaves  one  place  and  appears  in  another, 
than  why  a  cold  body  grows  warm?  Granted  that  we 
had  a  perfect  knowledge  of  the  mechanical  processes 
of  nature,  could  we  and  should  we,  for  that  reason, 
put  out  of  the  world  all  other  processes  that  we  do  not 
understand?  On  this  principle  it  would  really  be  the 
simplest  course  to  deny  the  existence  of  the  whole 
world.  This  is  the  point  at  which  the  Eleatics  ulti- 
mately arrived,  and  the  school  of  Herbart  stopped 
little  short  of  the  same  goal. 

Physics  treated  in  this  sense  supplies  us  simply 
with  a  diagram  of  the  world,  in  which  we  do  not  know 
reality  again.  It  happens,  in  fact,  to  men  who  give 
themselves  up  to  this  view  for  many  years,  that  the 
world  of  sense  from  which  they  start  as  a  province  of 
the  greatest  familiarity,  suddenly  becomes,  in  their 
eyes,  the  supreme  "world-riddle." 

Intelligible  as  it  is,  therefore,  that  the  efforts  of 
thinkers  have  always  been  bent  upon  the  "reduction 
of  all  physical  processes  to  the  motions  of  atoms,"  it 
must  yet  be  affirmed  that  this  is  a  chimerical  ideal. 
This  ideal  has  often  played  an  effective  part  in  popu- 
lar lectures,  but  in  the  workshop  of  the  serious  in- 
quirer it  has  discharged  scarcely  the  least  function. 
What  has  really  been  achieved  in  mechanical  physics 
is  either  the  elucidation  of  physical  processes  by  more 


160          ON  THE  CONSERVATION  OF  ENERGY. 

familiar  mechanical  analogies,  (for  example,  the  theories 
of  light  and  of  electricity,)  or  the  exact  quantitative 
ascertainment  of  the  connexion  of  mechanical  pro- 
cesses with  other  physical  processes,  for  example,  the 
results  of  thermodynamics. 

III.    THE  PRINCIPLE  OF  ENERGY  IN  PHYSICS. 

We  can  know  only  from  experience  that  mechanical 
processes  produce  other  physical  transformations,  or 
vice  versa.  The  attention  was  first  directed  to  the  con- 
nexion of  mechanical  processes,  especially  the  per- 
formance of  work,  with  changes  of  thermal  conditions 
by  the  invention  of  the  steam-engine,  and  by  its  great 
technical  importance.  Technical  interests  and  the 
need  of  scientific  lucidity  meeting  in  the  mind  of  S. 
Carnot  led  to  the  remarkable  development  from  which 
thermodynamics  flowed.  It  is  simply  an  accident  of 
history  that  the  development  in  question  was  not  con- 
nected with  the  practical  applications  of  electricity. 

In  the  determination  of  the  maximum  quantity  of 
work  that,  generally,  a  heat-machine,  or,  to  take  a 
special  case,  a  steam-engine,  can  perform  with  the 
expenditure  of  a  given  amount  of  heat  of  combustion, 
Carnot  is  guided  by  mechanical  analogies.  A  body  can 
do  work  on  being  heated,  by  expanding  under  pressure. 
But  to  do  this  the  body  must  receive  heat  from  a  hotter 
body.  Heat,  therefore,  to  do  work,  must  pass  from  a 
hotter  body  to  a  colder  body,  just  as  water  must  fall 
from  a  higher  level  to  a  lower  level  to  put  a  mill-wheel 


ON  THE  CONSERVATION  OF  ENERGY.          161 

in  motion.  Differences  of  temperature,  accordingly, 
represent  forces  able  to  do  work  exactly  as  do  differ- 
ences of  height  in  heavy  bodies.  Carnot  pictures  to 
himself  an  ideal  process  in  which  no  heat  flows  away 
unused,  that  is,  without  doing  work.  With  a  given  ex- 
penditure of  heat,  accordingly,  this  process  furnishes 
the  maximum  of  work.  An  analogue  of  the  process 
would  be  a  mill-wheel  which  scooping  its  water  out  of 
a  higher  level  would  slowly  carry  it  to  a  lower  level 
without  the  loss  of  a  drop.  A  peculiar  property  of  the 
process  is,  that  with  the  expenditure  of  the  same  work 
the  water  can  be  raised  again  exactly  to  its  original 
level.  This  property  of  reversibility  is  also  shared  by 
the  process  of  Carnot.  His  process  also  can  be  re- 
versed by  the  expenditure  of  the  same  amount  of  work, 
and  the  heat  again  brought  back  to  its  original  tem- 
perature level. 

Suppose,  now,  we  had  two  different  reversible  pro- 
cesses A,  B,  such  that  in  A  a  quantity  of  heat,  Q, 
flowing  off  from  the  temperature  /x  to  the  lower  tem- 
perature /2  should  perform  the  work  W,  but  in  B  under 
the  same  circumstances  it  should  perform  a  greater 
quantity  of  work  W+  W;  then,  we  could  join  B  in 
the  sense  assigned  and  A  in  the  reverse  sense  into  a 
single  process.  Here  A  would  reverse  the  transforma- 
tion of  heat  produced  by  B  and  would  leave  a  surplus 
of  work  W'y  produced,  so  to  speak,  from  nothing. 
The  combination  would  present  a  perpetual  motion. 

With  the  feeling,  now,  that  it  makes  little  differ- 


i62  ON  THE  CONSERVATION  OF  ENERGY, 

ence  whether  the  mechanical  laws  are  broken  directly 
or  indirectly  (by  processes  of  heat),  and  convinced  of 
the  existence  of  a  universal  law-ruled  connexion  of  na- 
ture, Carnot  here  excludes  for  the  first  time  from  the 
province  of  general  physics  the  possibility  of  a  per- 
petual motion.  But  it  follows,  then,  that  the  quantity 
of  work  W,  produced  by  the  passage  of  a  quantity  of  heat 
Q  from  a  temperature  t^  to  a  temperature  /2,  is  inde- 
pendent of  the  nature  of  the  substances  as  also  of  the  char- 
acter of  the  process,  so  far  as  that  is  unaccompanied  by 
loss,  but  is  wholly  dependent  upon  the  temperature  t^,  /2. 
This  important  principle  has  been  fully  confirmed 
by  the  special  researches  of  Carnot  himself  (1824),  of 
Clapeyron  (1834),  an(*  of  Sir  William  Thomson  (1849), 
now  Lord  Kelvin.  The  principle  was  reached  without 
any  assumption  whatever  concerning  the  nature  of  heat, 
simply  by  the  exclusion  of  a  perpetual  motion.  Carnot, 
it  is  true,  was  an  adherent  of  the  theory  of  Black,  ac- 
cording to  which  the  sum-total  of  the  quantity  of  heat 
in  the  world  is  constant,  but  so  far  as  his  investiga- 
tions have  been  hitherto  considered  the  decision  on 
this  point  is  of  no  consequence.  Carnot's  principle 
led  to  the  most  remarkable  results.  W.  Thomson 
(1848)  founded  upon  it  the  ingenious  idea  of  an  "ab- 
solute "  scale  of  temperature.  James  Thomson  (1849) 
conceived  a  Carnot  process  to  take  place  with  water 
freezing  under  pressure  and,  therefore,  performing 
work.  He  discovered,  thus,  that  the  freezing  point  is 
lowered  0-0075°  Celsius  by  every  additional  atmos- 


ON  THE  CONSERVATION  OF  ENERGY.  163 

phere  of  pressure.  This  is  mentioned  merely  as  an 
example. 

About  twenty  years  after  the  publication  of  Car- 
not's  book  a  further  advance  was  made  by  J.  R.  Mayer 
and  J.  P.  Joule.  Mayer,  while  engaged  as  a  physi- 
cian in  the  service  of  the  Dutch,  observed,  during  a 
process  of  bleeding  in  Java,  an  unusual  redness  of  the 
venous  blood.  In  agreement  with  Liebig's  theory  of 
animal  heat  he  connected  this  fact  with  the  diminished 
loss  of  heat  in  warmer  climates,  and  with  the  dimin- 
ished expenditure  of  organic  combustibles.  The  total 
expenditure  of  heat  of  a  man  at  rest  must  be  equal  to 
the  total  heat  of  combustion.  But  since  all  organic  ac- 
tions, even  the  mechanical  actions,  must  be  set  down 
to  the  credit  of  the  heat  of  combustion,  some  connex- 
ion must  exist  between  mechanical  work  and  expendi- 
ture of  heat. 

Joule  started  from  quite  similar  convictions  con- 
cerning the  galvanic  battery.  A  heat  of  association 
equivalent  to  the  consumption  of  the  zinc  can  be  made 
to  appear  in  the  galvanic  cell.  If  a  current  is  set  up, 
a  part  of  this  heat  appears  in  the  conductor  of  the 
current.  The  interposition  of  an  apparatus  for  the 
decomposition  of  water  causes  a  part  of  this  heat  to 
disappear,  which  on  the  burning  of  the  explosive  gas 
formed,  is  reproduced.  If  the  current  runs  an  elec- 
tromotor, a  portion  of  the  heat  again  disappears,  which, 
on  the  consumption  of  the  work  by  friction,  again 
makes  its  appearance.  Accordingly,  both  the  heat 


164  ON  THE  CONSERVATION  OF  ENERGY, 

produced  and  the  work  produced,  appeared  to  Joule 
also  as  connected  with  the  consumption  of  material. 
The  thought  was  therefore  present,  both  to  Mayer  and 
to  Joule,  of  regarding  heat  and  work  as  equivalent 
quantities,  so  connected  with  each  other  that  what  is 
lost  in  one  form  universally  appears  in  another.  The 
result  of  this  was  a  substantial  conception  of  heat  and 
of  work,  and  ultimately  a  substantial  conception  of  en- 
ergy. Here  every  physical  change  of  condition  is  re- 
garded as  energy,  the  destruction  of  which  generates 
work  or  equivalent  heat.  An  electric  charge,  for  ex- 
ample, is  energy. 

In  1842  Mayer  had  calculated  from  the  physical 
constants  then  universally  accepted  that  by  the  disap- 
pearance of  one  kilogramme-calorie  365  kilogramme- 
metres  of  work  could  be  performed,  and  vice  versa. 
Joule,  on  the  other  hand,  by  a  long  series  of  delicate 
and  varied  experiments  beginning  in  1843  ultimately 
determined  the  mechanical  equivalent  of  the  kilo- 
gramme-calorie, more  exactly,  as  425  kilogramme- 
metres. 

If  we  estimate  every  change  of  physical  condition 
by  the  mechanical  work  which  can  be  performed  upon 
the  disappearance  of  that  condition,  and  call  this  meas- 
ure energy,  then  we  can  measure  all  physical  changes 
of  condition,  no  matter  how  different  they  may  be, 
with  the  same  common  measure,  and  say  :  the  sum- 
total  of  all  energy  remains  constant.  This  is  the  form  that 
the  principle  of  excluded  perpetual  motion  received  at 


ON  THE  CONSERVATION  OF  ENERGY,          165 

the  hands  of  Mayer,  Joule,  Helmholtz,  and  W.  Thom- 
son in  its  extension  to  the  whole  domain  of  physics. 
After  it  had  been  proved  that  heat  must  disappear 
if  mechanical  work  was  to  be  done  at  its  expense, 
Carnot's  principle  could  no  longer  be  regarded  as  a 
complete  expression  of  the  facts.  Its  improved  form 
was  first  given,  in  1850,  by  Clausius,  whom  Thomson 
followed  in  1851.  It  runs  thus  :  "  If  a  quantity  of  heat 
Q'  is  transformed  into  work  in  a  reversible  process, 
another  quantity  of  heat  Q  of  the  absolute*  tempera- 
ture 7\  is  lowered  to  the  absolute  temperature  T2." 
Here  Q  is  dependent  only  on  Q,  Tlf  T2,  but  is  inde- 
pendent of  the  substances  used  and  of  the  character  of 
the  process,  so  far  as  that  is  unaccompanied  by  loss. 
Owing  to  this  last  fact,  it  is  sufficient  to  find  the  rela- 
tion which  obtains  for  some  one  well-known  physical 
substance,  say  a  gas,  and  some  definite  simple  pro- 
cess. The  relation  found  will  be  the  one  that  holds 
generally.  We  get,  thus, 


(i) 


that  is,  the  quotient  of  the  available  heat  @  trans- 
formed into  work  divided  by  the  sum  of  the  trans- 
formed and  transferred  heats  (the  total  sum  used),  the 
so-called  economical  coefficient  of  the  process,  is, 


*  By  this  is  meant  the  temperature  of  a  Celsius  scale,  the  uero  of  which  is 
2730  below  the  melting-point  of  ice. 


166          ON  THE  CONSERVATION  OF  ENERGY, 


IV.   THE  CONCEPTIONS  OF  HEAT. 

When  a  cold  body  is  put  in  contact  with  a  warm 
body  it  is  observed  that  the  first  body  is  warmed  and 
that  the  second  body  is  cooled.  We  may  say  that  the 
first  body  is  warmed  at  the  expense  of  the  second  body. 
This  suggests  the  notion  of  a  thing,  or  heat-substance, 
which  passes  from  the  one  body  to  the  other.  If  two 
masses  of  water  m,  m',  of  unequal  temperatures,  be 
put  together,  it  will  be  found,  upon  the  rapid  equali- 
sation of  the  temperatures,  that  the  respective  changes 
of  temperatures  u  and  u'  are  inversely  proportional  to 
the  masses  and  of  opposite  signs,  so  that  the  algebra- 
ical sum  of  the  products  is, 

M  u  -j-  m'  u'=  0. 

Black  called  the  products  m  u,  m'  u',  which  are  decisive 
for  our  knowledge  of  the  process,  quantities  of  heat. 
We  may  form  a  very  clear  picture  of  these  products 
by  conceiving  them  with  Black  as  measures  of  the 
quantities  of  some  substance.  But  the  essential  thing 
is  not  this  picture  but  the  constancy  of  the  sum  of  these 
products  in  simple  processes  of  conduction.  If  a  quan- 
tity of  heat  disappears  at  one  point,  an  equally  large 
quantity  will  make  its  appearance  at  some  other  point. 
The  retention  of  this  idea  leads  to  the  discovery  of 
specific  heat.  Black,  finally,  perceives  that  also  some- 
thing else  may  appear  for  a  vanished  quantity  of  heat, 
namely :  the  fusion  or  vaporisation  of  a  definite  quan- 


ON  THE  CONSERVATION  OF  ENERGY,          167 

tity  of  matter.  He  adheres  here  still  to  this  favorite 
view,  though  with  some  freedom,  and  considers  the 
vanished  quantity  of  heat  as  still  present,  but  as  latent. 

The  generally  accepted  notion  of  a  caloric,  or  heat- 
stuff,  was  strongly  shaken  by  the  work  of  Mayer  and 
Joule.  If  the  quantity  of  heat  can  be  increased  and 
diminished,  people  said,  heat  cannot  be  a  substance, 
but  must  be  a  motion.  The  subordinate  part  of  this 
statement  has  become  much  more  popular  than  all  the 
rest  of  the  doctrine  of  energy.  But  we  may  convince 
ourselves  that  the  motional  conception  of  heat  is  now 
as  unessential  as  was  formerly  its  conception  as  a  sub- 
stance. Both  ideas  were  favored  or  impeded  solely 
by  accidental  historical  circumstances.  It  does  not 
follow  that  heat  is  not  a  substance  from  the  fact  that 
a  mechanical  equivalent  exists  for  quantity  of  heat. 
We  will  make  this  clear  by  the  following  question 
which  bright  students  have  sometimes  put  to  me.  Is 
there  a  mechanical  equivalent  of  electricity  as  there  is 
a  mechanical  equivalent  of  heat  ?  Yes,  and  no.  There 
is  no  mechanical  equivalent  of  quantity  of  electricity 
as  there  is  an  equivalent  of  quantity  of  heat,  because 
the  same  quantity  of  electricity  has  a  very  different 
capacity  for  work,  according  to  the  circumstances  in 
which  it  is  placed ;  but  there  is  a  mechanical  equiv- 
alent of  electrical  energy. 

Let  us  ask  another  question.  Is  there  a  mechan- 
ical equivalent  of  water  ?  No,  there  is  no  mechanical 
equivalent  of  quantity  of  water,  but  there  is  a  me- 


168          ON  THE  CONSERVATION  OF  ENERGY, 

chanical  equivalent  of  weight  of  water  multiplied  by 
its  distance  of  descent. 

When  a  Ley  den  jar  is  discharged  and  work  thereby 
performed,  we  do  not  picture  to  ourselves  that  the 
quantity  of  electricity  disappears  as  work  is  done,  but 
we  simply  assume  that  the  electricities  come  into  dif- 
ferent positions,  equal  quantities  of  positive  and  nega- 
tive electricity  being  united  with  one  another. 

What,  now,  is  the  reason  of  this  difference  of  view 
in  our  treatment  of  heat  and  of  electricity  ?  The  rea- 
son is  purely  historical,  wholly  conventional,  and,  what 
is  still  more  important,  is  wholly  indifferent.  I  may 
be  allowed  to  establish  this  assertion 

In  1785  Coulomb  constructed  his  torsion  balance, 
by  which  he  was  enabled  to  measure  the  repulsion  of 
electrified  bodies.  Suppose  we  have  two  small  balls, 
A,  B,  which  over  their  whole  extent  are  similarly 
electrified.  These  two  balls  will  exert  on  one  another, 
at  a  certain  distance  r  of  their  centres,  a  certain  re- 
pulsion /.  We  bring  into  contact  with  B  now  a  ball 
C,  suffer  both  to  be  equally  electrified,  and  then  meas- 
ure the  repulsion  of  B  from  A  and  of  C  from  A  at  the 
same  distance  r.  The  sum  of  these  repulsions  is  again 
p.  Accordingly  something  has  remained  constant. 
If  M  e  ascribe  this  effect  to  a  substance,  then  we  infer 
naturally  its  constancy.  But  the  essential  point  of  the 
exposition  is  the  divisibility  of  the  electric  force/  and 
not  the  simile  of  substance. 

In  1838  Riess  constructed  his  electrical  air-thermom- 


ON  THE  CONSERVATION  OF  ENERGY.          169 

eter  (the  thermoelectrometer).  This  gives  a  measure 
of  the  quantity  of  heat  produced  by  the  discharge  of 
jars.  This  quantity  of  heat  is  not  proportional  to  the 
quantity  of  electricity  contained  in  the  jar  by  Cou- 
lomb's measure,  but  if  Q  be  this  quantity  and  C  be  the 
capacity,  is  proportional  to  Q2/2C,  or,  more  simply 
still,  to  the  energy  of  the  charged  jar.  If,  now,  we 
discharge  the  jar  completely  through  the  thermome- 
ter, we  obtain  a  certain  quantity  of  heat,  W.  But  if 
we  make  the  discharge  through  the  thermometer  into 
a  second  jar,  we  obtain  a  quantity  less  than  W.  But  we 
may  obtain  the  remainder  by  completely  discharging 
both  jars  through  the  air-thermometer,  when  it  will 
again  be  proportional  to  the  energy  of  the  two  jars.  On 
the  first,  incomplete  discharge,  accordingly,  a  part  of 
the  electricity's  capacity  for  work  was  lost. 

When  the  charge  of  a  jar  produces  heat  its  energy 
is  changed  and  its  value  by  Riess's  thermometer  is  de- 
creased. But  by  Coulomb's  measure  the  quantity  re- 
mains unaltered. 

Now  let  us  imagine  that  Riess's  thermometer  had 
been  invented  before  Coulomb's  torsion  balance,  which 
is  not  a  difficult  feat,  since  both  inventions  are  indepen- 
dent of  each  other  ;  what  would  be  more  natural  than 
that  the  "quantity"  of  electricity  contained  in  a  jar 
should  be  measured  by  the  heat  produced  in  the  ther- 
mometer ?  But  then,  this  so-called  quantity  of  elec- 
tricity would  decrease  on  the  production  of  heat  or  on 
the  performance  of  work,  whereas  it  now  remains  un- 


170          ON  THE  CONSERVATION  OF  ENERGY. 

changed ;  in  that  case,  therefore,  electricity  would  not 
be  a  substance  but  a  motion,  whereas  now  it  is  still  a 
substance.  The  reason,  therefore,  why  we  have  other 
notions  of  electricity  than  we  have  of  heat,  is  purely 
historical,  accidental,  and  conventional. 

This  is  also  the  case  with  other  physical  things. 
Water  does  not  disappear  when  work  is  done.  Why? 
Because  we  measure  quantity  of  water  with  scales,  just 
as  we  do  electricity.  But  suppose  the  capacity  of 
water  for  work  were  called  quantity,  and  had  to  be 
measured,  therefore,  by  a  mill  instead  of  by  scales ; 
then  this  quantity  also  would  disappear  as  it  per- 
formed the  work.  It  may,  now,  be  easily  conceived 
that  many  substances  are  not  so  easily  got  at  as  water. 
In  that  case  we  should  be  unable  to  carry  out  the  one 
kind  of  measurement  with  the  scales  whilst  many  other 
modes  of  measurement  would  still  be  left  us. 

In  the  case  of  heat,  now,  the  historically  established 
measure  of  "quantity"  is  accidentally  the  work- value 
of  the  heat.  Accordingly,  its  quantity  disappears  when 
work  is  done.  But  that  heat  is  not  a  substance  follows 
from  this  as  little  as  does  the  opposite  conclusion  that 
it  is  a  substance.  In  Black's  case  the  quantity  of  heat 
remains  constant  because  the  heat  passes  into  no  other 
form  of  energy. 

If  any  one  to-day  should  still  wish  to  think  of  heat 
as  a  substance,  we  might  allow  that  person  this  liberty 
with  little  ado.  He  would  only  have  to  assume  that 
that  which  we  call  quantity  of  heat  was  the  energy  of 


OAT  THE  CONSERVATION  OF  ENERGY.          171 

a  substance  whose  quantity  remained  unaltered,  but 
whose  energy  changed.  In  point  of  fact  we  might 
much  better  say,  in  analogy  with  the  other  terms  of 
physics,  energy  of  heat,  instead  of  quantity  of  heat. 

When  we  wonder,  therefore,  at  the  discovery  that 
heat  is  motion,  we  wonder  at  something  that  was  never 
discovered.  It  is  perfectly  indifferent  and  possesses 
not  the  slightest  scientific  value,  whether  we  think  of 
heat  as  a  substance  or  not.  The  fact  is,  heat  behaves 
in  some  connexions  like  a  substance,  in  others  not. 
Heat  is  latent  in  steam  as  oxygen  is  latent  in  water. 

V.  THE  CONFORMITY  IN  THE  DEPORTMENT  OF  THE 
ENERGIES. 

The  foregoing  reflexions  will  gain  in  lucidity  from 
a  consideration  of  the  conformity  which  obtains  in  the 
behavior  of  all  energies,  a  point  to  which  I  called  at- 
tention long  ago.* 

A  weight  P  at  a  height  H^  represents  an  energy 
W1=PJ71.  If  we  suffer  the  weight  to  sink  to  a  lower 
height  J72,  during  which  work  is  done,  and  the  work 
done  is  employed  in  the  production  of  living  force, 
heat,  or  an  electric  charge,  in  short,  is  transformed, 
then  the  energy  Wz  —PHZ  is  still  left.  The  equation 
subsists 

5=5 (2) 

*I  first  drew  attention  to  this  fact  in  my  treatise  Utbtr  dit  Erhalt»nS  dtr 
Arbeit,  Prague,  1872.     Before  this,  Zeuner  had  pointed  out  the  analog; 
tween  mechanical  and  thermal  energy.     I  have  given  a  more  extensive  de 
opment  of  this  idea  in  a  communication  to  the  SitzMnfsberickte  der  Wiener 


172          ON  THE  CONSERVATION  OF  ENERGY. 

or,  denoting  the  transformed  energy  by  W=  W^  —  Wz 
and  the  transferred  energy,  that  transported  to  the 
lower  level,  by  W=W2, 


W~ 

an  equation  in  all  respects  analogous  to  equation  (i) 
at  page  165.  The  property  in  question,  therefore,  is 
by  no  means  peculiar  to  heat.  Equation  (2)  gives  the 
relation  between  the  energy  taken  from  the  higher 
level  and  that  deposited  on  the  lower  level  (the  energy 
left  behind)  ;  it  says  that  these  energies  are  propor- 
tional to  the  heights  of  the  levels.  An  equation  analo- 
gous to  equation  (2)  may  be  set  up  for  every  form  of 
energy  ;  hence  the  equation  which  corresponds  to 
equation  (3),  and  so  to  equation  (i),  may  be  regarded 
as  valid  for  every  form.  For  electricity,  for  example, 
H^,  H2  signify  the  potentials. 

When  we  observe  for  the  first  time  the  agreement 
here  indicated  in  the  transformative  law  of  the  ener- 
gies, it  appears  surprising  and  unexpected,  for  we  do 
not  perceive  at  once  its  reason.  But  to  him  who  pur- 
sues the  comparative  historical  method  that  reason 
will  not  long  remain  a  secret. 

Since  Galileo,  mechanical  work,  though  long  under 
a  different  name,  has  been  a  fundamental  concept  of 
mechanics,  as  also  a  very  important  notion  in  the  ap- 
plied sciences.  The  transformation  of  work  into  liv- 

Akademie,  December,  1892,  entitled  Geschichte  und  Kritik  des  Carnof  schen 
Warmegesetzes.  Compare  also  the  works  of  Popper  (1884),  Helm  (1887), 
Wronsky  (1888),  and  Ostwald  (1892). 


ON  THE  CONSERVATION  OF  ENERGY.          173 

ing  force,  and  of  living  force  into  work,  suggests  di- 
rectly the  notion  of  energy — the  idea  having  been  first 
fruitfully  employed  by  Huygens,  although  Thomas 
Young  first  called  it  by  the  name  of  "energy."  Let 
us  add  to  this  the  constancy  of  weight  (really  the  con- 
stancy of  mass)  and  we  shall  see  that  with  respect  to 
mechanical  energy  it  is  involved  in  the  very  definition 
of  the  term  that  the  capacity  for  work  or  the  potential 
energy  of  a  weight  is  proportional  to  the  height  of  the 
level  at  which  it  is,  in  the  geometrical  sense,  and  that 
it  decreases  on  the  lowering  of  the  weight,  on  trans- 
formation, proportionally  to  the  height  of  the  level. 
The  zero  level  here  is  wholly  arbitrary.  With  this, 
equation  (2)  is  given,  from  which  all  the  other  forms 
follow. 

When  we  reflect  on  the  tremendous  start  which 
mechanics  had  over  the  other  branches  of  physics,  it 
is  not  to  be  wondered  at  that  the  attempt  was  always 
made  to  apply  the  notions  of  that  science  wherever 
this  was  possible.  Thus  the  notion  of  mass,  for  ex- 
ample, was  imitated  by  Coulomb  in  the  notion  of 
quantity  of  electricity.  In  the  further  development 
of  the  theory  of  electricity,  the  notion  of  work  was 
likewise  immediately  introduced  in  the  theory  of  po- 
tential, and  heights  of  electrical  level  were  measured 
by  the  work  of  unit  of  quantity  raised  to  that  level. 
But  with  this  the  preceding  equation  with  all  its  con- 
sequences is  given  for  electrical  energy.  The  case  with 
the  other  energies  was  similar. 


174  ON  THE  CONSERVATION  OF  ENERGY, 

Thermal  energy,  however,  appears  as  a  special 
case.  Only  by  the  peculiar  experiments  mentioned 
could  it  be  discovered  that  heat  is  an  energy.  But  the 
measure  of  this  energy  by  Black's  quantity  of  heat  is 
the  outcome  of  fortuitous  circumstances.  In  the  first 
place,  the  accidental  slight  variability  of  the  capacity 
for  heat  c  with  the  temperature,  and  the  accidental 
slight  deviation  of  the  usual  thermometrical  scales 
from  the  scale  derived  from  the  tensions  of  gases,  brings 
it  about  that  the  notion  "  quantity  of  heat  "  can  be  set 
up  and  that  the  quantity  of  heat  ct  corresponding  to  a 
difference  of  temperature  /  is  nearly  proportional  to 
the  energy  of  the  heat.  It  is  a  quite  accidental  his- 
torical circumstance  that  Amontons  hit  upon  the  idea 
of  measuring  temperature  by  the  tension  of  a  gas.  It 
is  certain  in  this  that  he  did  not  think  of  the  work  of 
the  heat.*  But  the  numbers  standing  for  tempera- 
ture, thus,  are  made  proportional  to  the  tensions  of 
gases,  that  is,  to  the  work  done  by  gases,  with  other- 
wise equal  changes  of  volume.  It  thus  happens  that 
temperature  heights  and  level  heights  of  work  are  pro- 
portional to  one  another. 

If  properties  of  the  thermal  condition  varying 
greatly  from  the  tensions  of  gases  had  been  chosen, 
this  relation  would  have  assumed  very  complicated 
forms,  and  the  agreement  between  heat  and  the  other 
energies  above  considered  would  not  subsist.  It  is 

*Sir  William  Thomson  first  consciously  and  intentionally  introduced 
(1848,  1851)  a  mechanical  measure  of  temperature  similar  to  the  electric  meas- 
ure of  potential. 


ON  THE  CONSERVATION  OF  ENERGY.          175 

very  instructive  to  reflect  upon  this  point.  A  natural 
law,  therefore,  is  not  implied  in  the  conformity  of  the 
behavior  of  the  energies,  but  this  conformity  is  rather 
conditioned  by  the  uniformity  of  our  modes  of  con- 
ception and  is  also  partly  a  matter  of  good  fortune. 

VI.  THE  DIFFERENCES  OF  THE  ENERGIES  AND  THE 
LIMITS  OF  THE  PRINCIPLE  OF  ENERGY. 

Of  every  quantity  of  heat  Q  which  does  work  in  a 
reversible  process  (one  unaccompanied  by  loss)  be- 
tween the  absolute  temperatures  Tlt  T2,  only  the  por- 
tion 


is  transformed  into  work,  while  the  remainder  is  trans- 
ferred to  the  lower  temperature-level  T2.  This  trans- 
ferred portion  can,  upon  the  reversal  of  the  process, 
with  the  same  expenditure  of  work,  again  be  brought 
back  to  the  level  T^.  But  if  the  process  is  not  rever- 
sible, then  more  heat  than  in  the  foregoing  case  flows 
to  the  lower  level,  and  the  surplus  can  no  longer  be 
brought  back  to  the  higher  level  T2  without  some  spe- 
cial expenditure.  W.  Thomson  (1852),  accordingly, 
drew  attention  to  the  fact,  that  in  all  non-reversible, 
that  is,  in  all  real  thermal  processes,  quantities  of  heat 
are  lost  for  mechanical  work,  and  that  accordingly  a 
dissipation  or  waste  of  mechanical  energy  is  taking 
place.  In  all  cases,  heat  is  only  partially  transformed 
into  work,  but  frequently  work  is  wholly  transformed 


176          OAT  THE  CONSERVATION  OF  ENERGY. 

into  heat.  Hence,  a  tendency  exists  towards  a  diminu- 
tion of  the  mechanical  energy  and  towards  an  increase 
of  the  thermal  energy  of  the  world. 

For  a  simple,  closed  cyclical  process,  accompanied 
by  no  loss,  in  which  the  quantity  of  heat  Q^  is  taken 
from  the  level  TI}  and  the  quantity  Q2  is  deposited 
upon  the  level  T2,  the  following  relation,  agreeably  to 
equation  (2),  exists, 


Similarly,   for  any  number  of  compound  reversible 
cycles  Clausius  finds  the  algebraical  sum 


and  supposing  the  temperature  to  change  continuously, 


Here  the  elements  of  the  quantities  of  heat  deducted 
from  a  given  level  are  reckoned  negative,  and  the  ele- 
ments imparted  to  it,  positive.  If  the  process  is  not 
reversible,  then  expression  (4),  which  Clausius  calls 
entropy,  increases.  In  actual  practice  this  is  always 
the  case,  and  Clausius  finds  himself  led  to  the  state- 
ment : 

1.  That  the  energy  of  the  world  remains  constant. 

2.  That  the  entropy  of  the  world  tends  toward  a 
maximum. 

Once  we  have  noted  the  above-indicated  conform- 
ity in  the  behavior  of  different  energies,  the  peculiarity 


ON  THE  CONSERVATION  OF  ENERGY.          177 

of  thermal  energy  here  mentioned  must  strike  us. 
Whence  is  this  peculiarity  derived,  for,  generally  every 
energy  passes  only  partly  into  another  form,  which  is 
also  true  of  thermal  energy  ?  The  explanation  will  be 
found  in  the  following. 

Every  transformation  of  a  special  kind  of  energy^ 
is  accompanied  with  a  fall  of  potential  of  that  particu- 
lar kind  of  energy,  including  heat.  But  whilst  for  the 
other  kinds  of  energy  a  transformation  and  therefore  a 
loss  of  energy  on  the  part  of  the  kind  sinking  in  po- 
tential is  connected  with  the  fall  of  the  potential,  with 
heat  the  case  is  different.  Heat  can  suffer  a  fall  of 
potential  without  sustaining  a  loss  of  energy,  at  least 
according  to  the  customary  mode  of  estimation.  If  a 
weight  sinks,  it  must  create  perforce  kinetic  energy, 
or  heat,  or  some  other  form  of  energy.  Also,  an  elec- 
trical charge  cannot  suffer  a  fall  of  potential  without 
loss  of  energy,  i.  e.,  without  transformation.  But  heat 
can  pass  with  a  fall  of  temperature  to  a  body  of  greater 
capacity  and  the  same  thermal  energy  still  be  pre- 
served, so  long  as  we  regard  every  quantity  of  heat  as 
energy.  This  it  is  that  gives  to  heat,  besides  its 
property  of  energy,  in  many  cases  the  character  of  a 
material  substance,  or  quantity. 

If  we  look  at  the  matter  in  an  unprejudiced  light, 
we  must  ask  if  there  is  any  scientific  sense  or  purpose 
in  still  considering  as  energy  a  quantity  of  heat  that 
can  no  longer  be  transformed  into  mechanical  work, 
(for  example,  the  heat  of  a  closed  equably  warmed 


178  ON  THE  CONSERVATION  OF  ENERGY. 

material  system).  The  principle  of  energy  certainly 
plays  in  this  case  a  wholly  superfluous  role,  which  is 
assigned  to  it  only  from  habit*  To  maintain  the  prin- 
ciple of  energy  in  the  face  of  a  knowledge  of  the  dissi- 
pation or  waste  of  mechanical  energy,  in  the  face  of 
the  increase  of  entropy  is  equivalent  almost  to  the 
liberty  which  Black  took  when  he  regarded  the  heat 
of  liquefaction  as  still  present  but  latent,  f  It  is  to  be 
remarked  further,  that  the  expressions  "energy  of  the 
world"  and  "entropy  of  the  world"  are  slightly  per- 
meated with  scholasticism.  Energy  and  entropy  are 
metrical  notions.  What  meaning  can  there  be  in  ap- 
plying these  notions  to  a  case  in  which  they  are  not 
applicable,  in  which  their  values  are  not  determin- 
ate? 

If  we  could  really  determine  the  entropy  of  the 
world  it  would  represent  a  true,  absolute  measure  of 
time.  In  this  way  is  best  seen  the  utter  tautology  of 
a  statement  that  the  entropy  of  the  world  increases 
with  the  time.  Time,  and  the  fact  that  certain  changes 
take  place  only  in  a  definite  sense,  are  one  and  the 
same  thing. 

*  Compare  my  Analysis  of  the  Sensations,  Jena,  1886  :  English  translation, 
Chicago,  1897. 

t  A  better  terminology  appears  highly  desirable  in  the  place  of  the  usual 
misleading  one.  Sir  William  Thomson  (1852)  appears  to  have  felt  this  need, 
and  it  has  been  clearly  expressed  by  F.  Wald  (1889).  We  should  call  the  work 
which  corresponds  to  a  vanished  quantity  of  heat  its  mechanical  substitution- 
value  ;  while  that  work  which  can  be  actually  performed  in  the  passage  of  a 
thermal  condition  A  to  a  condition  ff,  alone  deserves  the  name  of  the  energy- 
value  of  this  change  of  condition.  In  this  way  the  arbitrary  substantial  con- 
ception of  the  processes  would  be  preserved  and  misapprehensions  fore- 
stalled. 


ON  THE  CONSERVATION  OF  ENERGY.          179 


VII.    THE  SOURCES  OF  THE  PRINCIPLE  OF  ENERGY. 

We  are  now  prepared  to  answer  the  question,  What 
are  the  sources  of  the  principle  of  energy  ?  All  knowl- 
edge of  nature  is  derived  in  the  last  instance  from  ex- 
perience. In  this  sense  they  are  right  who  look  upon 
the  principle  of  energy  as  a  result  of  experience. 

Experience  teaches  that  the  sense-elements  afiyd — 
into  which  the  world  may  be  decomposed,  are  subject 
to  change.  It  tells  us  further,  that  certain  of  these 
elements  are  connected  with  other  elements,  so  that  they 
appear  and  disappear  together;  or,  that  the  appear- 
ance of  the  elements  of  one  class  is  connected  with  the 
disappearance  of  the  elements  of  the  other  class.  We 
will  avoid  here  the  notions  of  cause  and  effect  be- 
cause of  their  obscurity  and  equivocalness.  The  re- 
sult of  experience  may  be  expressed  as  follows :  The 
sensuous  elements  of  the  world  (a  f$y  d .  .  .  .)  show  them- 
selves to  be  interdependent.  This  interdependence  is 
best  represented  by  some  such  conception  as  is  in 
geometry  that  of  the  mutual  dependence  of  the  sides 
and  angles  of  a  triangle,  only  much  more  varied  and 
complex. 

As  an  example,  we  may  take  a  mass  of  gas  enclosed 
in  a  cylinder  and  possessed  of  a  definite  volume  («), 
which  we  change  by  a  pressure  (/?)  on  the  piston,  at 
the  same  time  feeling  the  cylinder  with  our  hand  and 


i8o          ON  THE  CONSERVATION  OF  ENERGY. 

receiving  a  sensation  of  heat  (y).  Increase  of  pres- 
sure diminishes  the  volume  and  increases  the  sensa- 
tion of  heat. 

The  various  facts  of  experience  are  not  in  all  re- 
spects alike.  Their  common  sensuous  elements  are 
placed  in  relief  by  a  process  of  abstraction  and  thus 
impressed  upon  the  memory.  In  this  way  the  expres- 
sion is  obtained  of  the  features  of  agreement  of  extensive 
groups  of  facts.  The  simplest  sentence  which  we  can 
utter  is,  by  the  very  nature  of  language,  an  abstraction 
of  this  kind.  But  account  must  also  be  taken  of  the 
differences  of  related  facts.  Facts  may  be  so  nearly  re- 
lated as  to  contain  the  same  kind  of  a  fly  ,  .  .,  but  the 
relation  be  such  that  the  afiy  .  .  .  of  the  one  differ 
from  the  a fly ...  of  the  other  only  by  the  number  of 
equal  parts  into  which  they  can  be  divided.  Such 
being  the  case,  if  rules  can  be  given  for  deducing/rom 
one  another  the  numbers  which  are  the  measures  of 
these  afty. . .,  then  we  possess  in  such  rules  the  most 
general  expression  of  a  group  of  facts,  as  also  that  ex- 
pression which  corresponds  to  all  its  differences.  This 
is  the  goal  of  quantitative  investigation. 

If  this  goal  be  reached  what  we  have  found  is  that 
between  the  a  fly. . .  of  a  group  of  facts,  or  better,  be- 
tween the  numbers  which  are  their  measures,  a  num- 
ber of  equations  exists.  The  simple  fact  of  change 
brings  it  about  that  the  number  of  these  equations 
must  be  smaller  than  the  number  of  the  afiy . . .  If 
the  former  be  smaller  by  one  than  the  latter,  then  one 


ON  THE  CONSERVATION  OF  ENERGY.  181 

portion  of  the  afiy...  is  uniquely  determined  by  the 
other  portion. 

The  quest  of  relations  of  this  last  kind  is  the  most 
important  function  of  special  experimental  research, 
because  we  are  enabled  by  it  to  complete  in  thought 
facts  that  are  only  partly  given.  It  is  self-evident  that 
only  experience  can  ascertain  that  between  the  a  fly . .  . 
relations  exist  and  of  what  kind  they  are.  Further, 
only  experience  can  tell  that  the  relations  that  exist 
between  the  a  fiy. . .  are  such  that  changes  of  them 
can  be  reversed.  If  this  were  not  the  fact  all  occasion 
for  the  enunciation  of  the  principle  of  energy,  as  is 
easily  seen,  would  be  wanting.  In  experience,  there- 
fore, is  buried  the  ultimate  well-spring  of  all  knowl- 
edge of  nature,  and  consequently,  in  this  sense,  also 
the  ultimate  source  of  the  principle  of  energy. 

But  this  does  not  exclude  the  fact  that  the  princi- 
ple of  energy  has  also  a  logical  root,  as  will  now  be 
shown.  Let  us  assume  on  the  basis  of  experience  that 
one  group  of  sensuous  elements  acfiy.  . .  determines 
uniquely  another  group  \^v...  Experience  further 
teaches  that  changes  of  a/3y...  can  be  reversed.  It 
is  then  a  logical  consequence  of  this  observation,  that 
every  time  that  <x/3y...  assume  the  same  values  this 
is  also  the  case  with  Xpv. . .  Or,  that  purely  period- 
ical changes  of  afiy...  can  produce  no  permanent 
changes  of  Ayuv...  If  the  group  A/*v...  is  a  me- 
chanical group,  then  a  perpetual  motion  is  excluded. 


i82  ON  THE  CONSERVATION  OF  ENERGY. 

It  will  be  said  that  this  is  a  vicious  circle,  which 
we  will  grant.  But  psychologically,  the  situation  is 
essentially  different,  whether  I  think  simply  of  the 
unique  determination  and  reversibility  of  events,  or 
whether  I  exclude  a  perpetual  motion.  The  attention 
takes  in  the  two  cases  different  directions  and  diffuses 
light  over  different  sides  of  the  question,  which  logi- 
cally of  course  are  necessarily  connected. 

Surely  that  firm,  logical  setting  of  the  thoughts  no- 
ticeable in  the  great  inquirers,  Stevinus,  Galileo,  and 
the  rest,  which,  consciously  or  instinctively,  was  sup- 
ported by  a  fine  feeling  for  the  slightest  contradictions, 
has  no  other  purpose  than  to  limit  the  bounds  of 
thought  and  so  exempt  it  from  the  possibility  of  error. 
In  this,  therefore,  the  logical  root  of  the  principle  of 
excluded  perpetual  motion  is  given,  namely,  in  that 
universal  conviction  which  existed  even  before  the  de- 
velopment of  mechanics  and  co-operated  in  that  de- 
velopment. 

It  is  perfectly  natural  that  the  principle  of  excluded 
perpetual  motion  should  have  been  first  developed  in 
the  simple  domain  of  pure  mechanics.  Towards  the 
transference  of  that  principle  into  the  domain  of  gen- 
eral physics  the  idea  contributed  much  that  all  phys- 
ical phenomena  are  mechanical  phenomena.  But  the 
foregoing  discussion  shows  how  little  essential  this 
notion  is.  The  issue  really  involved  is  the  recognition 
of  a  general  interconnexion  of  nature.  This  once  es- 
tablished, we  see  with  Carnot  that  it  is  indifferent 


ON  THE  CONSERVATION  OF  ENERGY.  183 

whether  the  mechanical  laws  are  broken  directly  or 
circuitously. 

The  principle  of  the  excluded  perpetual  motion  is 
very  closely  related  to  the  modern  principle  of  energy, 
but  it  is  not  identical  with  it,  for  the  latter  is  to  be 
deduced  from  the  former  only  by  means  of  a  definite 
formal  conception.  As  may  be  seen  from  the  preceding 
exposition,  the  perpetual  motion  can  be  excluded  with- 
out our  employing  or  possessing  the  notion  of  work. 
The  modern  principle  of  energy  results  primarily  from 
a  substantial  conception  of  work  and  of  every  change 
of  physical  condition  which  by  being  reversed  pro- 
duces work.  The  strong  need  of  such  a  conception, 
which  is  by  no  means  necessary,  but  in  a  formal  sense 
is  very  convenient  and  lucid,  is  exhibited  in  the  case 
of  J.  R.  Mayer  and  Joule.  It  was  before  remarked 
that  this  conception  was  suggested  to  both  inquirers 
by  the  observation  that  both  the  production  of  heat 
and  the  production  of  mechanical  work  were  connected 
with  an  expenditure  of  substance.  Mayer  says  :  "Ex 
nihilo  nil  fit,"  and  in  another  place,  "The  creation  or 
destruction  of  a  force  (work)  lies  without  the  province 
of  human  activity."  In  Joule  we  find  this  passage  : 
"It  is  manifestly  absurd  to  suppose  that  the  powers 
with  which  God  has  endowed  matter  can  be  destroyed." 

Some  writers  have  observed  in  such  statements  the 
attempt  at  a  metaphysical  establishment  of  the  doctrine 
of  energy.  But  we  see  in  them  simply  the  formal  need 
of  a  simple,  clear,  and  living  grasp  of  the  facts,  which 


184  ON  THE  CONSERVATION  OF  ENERGY. 

receives  its  development  in  practical  and  technical  life, 
and  which  we  carry  over,  as  best  we  can,  into  the 
province  of  science.  As  a  fact,  Mayer  writes  to  Grie- 
singer :  "  If,  finally,  you  ask  me  how  I  became  involved 
in  the  whole  affair,  my  answer  is  simply  this  :  Engaged 
during  a  sea  voyage  almost  exclusively  with  the  study 
of  physiology,  I  discovered  the  new  theory  for  the 
sufficient  reason  that  I  vividly  felt  the  need  of  it." 

The  substantial  conception  of  work  (energy)  is  by 
no  means  a  necessary  one.  And  it  is  far  from  true  that 
the  problem  is  solved  with  the  recognition  of  the  need 
of  such  a  conception.  Rather  let  us  see  how  Mayer 
gradually  endeavored  to  satisfy  that  need.  He  first 
regards  quantity  of  motion,  or  momemtum,  m  v,  as  the 
equivalent  of  work,  and  did  not  light,  until  later,  on 
the  notion  of  living  force  (*«#2/2).  In  the  province 
of  electricity  he  was  unable  to  assign  the  expression 
which  is  the  equivalent  of  work.  This  was  done  later 
by  Helmholtz.  The  formal  need,  therefore,  is  first 
present,  and  our  conception  of  nature  is  subsequently 
gradually  adapted  to  it. 

The  laying  bare  of  the  experimental,  logical,  and 
formal  root  of  the  present  principle  of  energy  will  per- 
haps contribute  much  to  the  removal  of  the  mysticism 
which  still  clings  to  this  principle.  With  respect  to 
our  formal  need  of  a  very  simple,  palpable,  substan- 
tial conception  of  the  processes  in  our  environment,  it 
remains  an  open  question  how  far  nature  corresponds 
to  that  need,  or  how  far  we  can  satisfy  it.  In  one 


ON  THE  CONSERVATION  OF  ENERGY.  185 

phase  of  the  preceding  discussions  it  would  seem  as 
if  the  substantial  notion  of  the  principle  of  energy,  like 
Black's  material  conception  of  heat,  has  its  natural 
limits  in  facts,  beyond  which  it  can  only  be  artificially 
adhered  to. 


THE  ECONOMICAL  NATURE  OF 
PHYSICAL  INQUIRY.* 


WHEN  the  human  mind,  with  its  limited  powers, 
attempts  to  mirror  in  itself  the  rich  life  of  the 
world,  of  which  it  is  itself  only  a  small  part,  and  which 
it  can  never  hope  to  exhaust,  it  has  every  reason  for 
proceeding  economically.  Hence  that  tendency,  ex- 
pressed in  the  philosophy  of  all  times,  to  compass  by 
a  few  organic  thoughts  the  fundamental  features  of 
reality.  "  Life  understands  not  death,  nor  death  life." 
So  spake  an  old  Chinese  philosopher.  Yet  in  his  un- 
ceasing desire  to  diminish  the  boundaries  of  the  in- 
comprehensible, man  has  always  been  engaged  in  at- 
tempts to  understand  death  by  life  and  life  by  death. 
Among  the  ancient  civilised  peoples,  nature  was 
filled  with  demons  and  spirits  having  the  feelings  and 
desires  of  men.  In  all  essential  features,  this  animistic 
view  of  nature,  as  Tylorf  has  aptly  termed  it,  is  shared 
in  common  by  the  fetish-worshipper  of  modern  Africa 

*  An  address  delivered  before  the  anniversary  meeting  of  the  Imperial 
Academy  of  Sciences,  at  Vienna,  May  25,  1882. 
}  Primitive  Culture. 


THE  ECONOMICAL  NATURE  OF  PHYSICS.      187 

and  the  most  advanced  nations  of  antiquity.  As  a 
theory  of  the  world  it  has  never  completely  disap- 
peared. The  monotheism  of  the  Christians  never  fully 
overcame  it,  no  more  than  did  that  of  the  Jews.  In 
the  belief  in  witchcraft  and  in  the  superstitions  of  the 
sixteenth  and  seventeenth  centuries,  the  centuries  of 
the  rise  of  natural  science,  it  assumed  frightful  path- 
ological dimensions.  Whilst  Stevinus,  Kepler,  and 
Galileo  were  slowly  rearing  the  fabric  of  modern  phys- 
ical science,  a  cruel  and  relentless  war  was  waged 
with  firebrand  and  rack  against  the  devils  that  glowered 
from  every  corner.  To-day  even,  apart  from  all  sur- 
vivals of  that  period,  apart  from  the  traces  of  fetish- 
ism which  still  inhere  in  our  physical  concepts,*  those 
very  ideas  still  covertly  lurk  in  the  practices  of  modern 
spiritualism. 

By  the  side  of  this  animistic  conception  of  the 
world,  we  meet  from  time  to  time,  in  different  forms, 
from  Democritus  to  the  present  day,  another  view, 
which  likewise  claims  exclusive  competency  to  com- 
prehend the  universe.  This  view  may  be  character- 
ised as  the  physico-mechanical  view  of  the  world.  To- 
day, that  view  holds,  indisputably,  the  first  place  in  the 
thoughts  of  men,  and  determines  the  ideals  and  the 
character  of  our  times.  The  coming  of  the  mind  of 
man  into  the  full  consciousness  of  its  powers,  in  the 
eighteenth  century,  was  a  period  of  genuine  disillu- 
sionment. It  produced  the  splendid  precedent  of  a  life 

•  Tylor,  loc.  cit. 


i88        THE  ECONOMICAL  NA  TURE  OF  PHYSICS, 

really  worthy  of  man,  competent  to  overcome  the  old 
barbarism  in  the  practical  fields  of  life ;  it  created  the 
Critique  of  Pure  Reason,  which  banished  into  the  realm 
of  shadows  the  sham-ideas  of  the  old  metaphysics  ;  it 
pressed  into  the  hands  of  the  mechanical  philosophy 
the  reins  which  it  now  holds. 

The  oft-quoted  words  of  the  great  Laplace,*  which 
I  will  now  give,  have  the  ring  of  a  jubilant  toast  to 
the  scientific  achievements  of  the  eighteenth  century : 
"A  mind  to  which  were  given  for  a  single  instant  all 
the  forces  of  nature  and  the  mutual  positions  of  all  its 
masses,  if  it  were  otherwise  powerful  enough  to  sub- 
ject these  problems  to  analysis,  could  grasp,  with  a 
single  formula,  the  motions  of  the  largest  masses  as 
well  as  of  the  smallest  atoms ;  nothing  would  be  un- 
certain for  it ;  the  future  and  the  past  would  lie  re- 
vealed before  its  eyes."  In  writing  these  words,  La- 
place, as  we  know,  had  also  in  mind  the  atoms  of  the 
brain.  That  idea  has  been  expressed  more  forcibly 
still  by  some  of  his  followers,  and  it  is  not  too  much 
to  say  that  Laplace's  ideal  is  substantially  that  of  the 
great  majority  of  modern  scientists. 

Gladly  do  we  accord  to  the  creator  of  the  Meca- 
nique  celeste  the  sense  of  lofty  pleasure  awakened  in 
him  by  the  great  success  of  the  Enlightenment,  to 
which  we  too  owe  our  intellectual  freedom.  But  to- 
day, with  minds  undisturbed  and  before  new  tasks,  it 


*Eisat  philosophique  sur  Us  probability.    6th  Ed.  Paris,  1840,  p.  4.    The 
necessary  consideration  of  the  initial  velocities  is  lacking  in  this  formulation. 


THE  ECONOMICAL  NATURE  OF  PHYSICS.       189 

becomes  physical  science  to  secure  itself  against  self- 
deception  by  a  careful  study  of  its  character,  so  that 
it  can  pursue  with  greater  sureness  its  true  objects. 
If  I  step,  therefore,  beyond  the  narrow  precincts  of  my 
specialty  in  this  discussion,  to  trespass  on  friendly 
neighboring  domains,  I  may  plead  in  my  excuse  that 
the  subject-matter  of  knowledge  is  common  to  all  do- 
mains of  research,  and  that  fixed,  sharp  lines  of  de- 
marcation cannot  be  drawn. 

The  belief  in  occult  magic  powers  of  nature  has 
gradually  died  away,  but  in  its  place  a  new  belief  has 
arisen,  the  belief  in  the  magical  power  of  science. 
Science  throws  her  treasures,  not  like  a  capricious 
fairy  into  the  laps  of  a  favored  few,  but  into  the  laps 
of  all  humanity,  with  a  lavish  extravagance  that  no 
legend  ever  dreamt  of !  Not  without  apparent  justice, 
therefore,  do  her  distant  admirers  impute  to  her  the 
power  of  opening  up  unfathomable  abysses  of  nature, 
to  which  the  senses  cannot  penetrate.  Yet  she  who 
came  to  bring  light  into  the  world,  can  well  dispense 
with  the  darkness  of  mystery,  and  with  pompous  show, 
which  she  needs  neither  for  the  justification  of  her 
aims  nor  for  the  adornment  of  her  plain  achievements. 

The  homely  beginnings  of  science  will  best  reveal 
to  us  its  simple,  unchangeable  character.  Man  ac- 
quires his  first  knowledge  of  nature  half-consciously 
and  automatically,  from  an  instinctive  habit  of  mimick- 
ing and  forecasting  facts  in  thought,  of  supplementing 
sluggish  experience  with  the  swift  wings  of  thought, 


igo        THE  ECONOMICAL  NATURE  OF  PHYSICS. 

at  first  only  for  his  material  welfare.  When  he  hears 
a  noise  in  the  underbrush  he  constructs  there,  just  as 
the  animal  does,  the  enemy  which  he  fears  ;  when  he 
sees  a  certain  rind  he  forms  mentally  the  image  of  the 
fruit  which  he  is  in  search  of ;  just  as  we  mentally  as- 
sociate a  certain  kind  of  matter  with  a  certain  line  in 
the  spectrum  or  an  electric  spark  with  the  friction  of  a 
piece  of  glass.  A  knowledge  of  causality  in  this  form 
certainly  reaches  far  below  the  level  of  Schopenhauer's 
pet  dog,  to  whom  it  was  ascribed.  It  probably  exists 
in  the  whole  animal  world,  and  confirms  that  great 
thinker's  statement  regarding  the  will  which  created 
the  intellect  for  its  purposes.  These  primitive  psych- 
ical functions  are  rooted  in  the  economy  of  our  organ- 
ism not  less  firmly  than  are  motion  and  digestion. 
Who  would  deny  that  we  feel  in  them,  too,  the  ele- 
mental power  of  a  long  practised  logical  and  physio- 
logical activity,  bequeathed  to  us  as  an  heirloom  from 
our  forefathers? 

Such  primitive  acts  of  knowledge  constitute  to-day 
the  solidest  foundation  of  scientific  thought.  Our  in- 
stinctive knowledge,  as  we  shall  briefly  call  it,  by  vir- 
tue of  the  conviction  that  we  have  consciously  and 
intentionally  contributed  nothing  to  its  formation,  con- 
fronts us  with  an  authority  and  logical  power  which 
consciously  acquired  knowledge  even  from  familiar 
sources  and  of  easily  tested  fallibility  can  never  possess. 
All  so-called  axioms  are  such  instinctive  knowledge. 
Not  consciously  gained  knowledge  alone,  but  powerful 


THE  ECONOMICAL  NATURE  OF  PHYSICS.       191 

intellectual  instinct,  joined  with  vast  conceptive  powers, 
constitute  the  great  inquirer.  The  greatest  advances 
of  science  have  always  consisted  in  some  successful 
formulation, in  clear,  abstract,  and  communicable  terms, 
of  what  was  instinctively  known  long  before,  and  of 
thus  making  it  the  permanent  property  of  humanity. 
By  Newton's  principle  of  the  equality  of  pressure  and 
counterpressure,  whose  truth  all  before  him  had  felt, but 
which  no  predecessor  had  abstractly  formulated,  me- 
chanics was  placed  by  a  single  stroke  on  a  higher  level. 
Our  statement  might  also  be  historically  justified  by 
examples  from  the  scientific  labors  of  Stevinus,  S. 
Carnot,  Faraday,  J.  R.  Mayer,  and  others. 

All  this,  however,  is  merely  the  soil  from  which 
science  starts.  The  first  real  beginnings  of  science 
appear  in  society,  particularly  in  the  manual  arts, 
where  the  necessity  for  the  communication  of  experi- 
ence arises.  Here,  where  some  new  discovery  is  to 
be  described  and  related,  the  compulsion  is  first  felt  of 
clearly  defining  in  consciousness  the  important  and 
essential  features  of  that  discovery,  as  many  writers 
can  testify.  The  aim  of  instruction  is  simply  the  sav- 
ing of  experience ;  the  labor  of  one  man  is  made  to 
take  the  place  of  that  of  another. 

The  most  wonderful  economy  of  communication  is 
found  in  language.  Words  are  comparable  to  type, 
which  spare  the  repetition  of  written  signs  and  thus 
serve  a  multitude  of  purposes ;  or  to  the  few  sounds 
of  which  our  numberless  different  words  are  composed. 


192        THE  ECONOMICAL  NATURE  OF  PHYSICS. 

Language,  with  its  helpmate,  conceptual  thought,  by 
fixing  the  essential  and  rejecting  the  unessential,  con- 
structs its  rigid  pictures  of  the  fluid  world  on  the  plan 
of  a  mosaic,  at  a  sacrifice  of  exactness  and  fidelity  but 
with  a  saving  of  tools  and  labor.  Like  a  piano-player 
with  previously  prepared  sounds,  a  speaker  excites  in 
his  listener  thoughts  previously  prepared,  but  fitting 
many  cases,  which  respond  to  the  speaker's  summons 
with  alacrity  and  little  effort. 

The  principles  which  a  prominent  political  econom- 
ist, E.  Hermann,*  has  formulated  for  the  economy  of 
the  industrial  arts,  are  also  applicable  to  the  ideas  of 
common  life  and  of  science.  The  economy  of  language 
is  augmented,  of  course,  in  the  terminology  of  science. 
With  respect  to  the  economy  of  written  intercourse 
there  is  scarcely  a  doubt  that  science  itself  will  realise 
that  grand  old  dream  of  the  philosophers  of  a  Uni- 
versal Real  Character.  That  time  is  not  far  distant. 
Our  numeral  characters,  the  symbols  of  mathematical 
analysis,  chemical  symbols,  and  musical  notes,  which 
might  easily  be  supplemented  by  a  system  of  color- 
signs,  together  with  some  phonetic  alphabets  now  in 
use,  are  all  beginnings  in  this  direction.  The  logical 
extension  of  what  we  have,  joined  with  a  use  of  the 
ideas  which  the  Chinese  ideography  furnishes  us,  will 
render  the  special  invention  and  promulgation  of  a 
Universal  Character  wholly  superfluous. 

The  communication  of  scientific  knowledge  always 

*  Princifien  der  Wirthschaftslehrc,  Vienna,  1873. 


THE  ECONOMICAL  NATURE  OF  PHYSICS.       193 

involves  description,  that  is,  a  mimetic  reproduction 
of  facts  in  thought,  the  object  of  which  is  to  replace 
and  save  the  trouble  of  new  experience.  Again,  to 
save  the  labor  of  instruction  and  of  acquisition,  con- 
cise, abridged  description  is  sought.  This  is  really  all 
that  natural  laws  are.  Knowing  the  value  of  the  ac- 
celeration of  gravity,  and  Galileo's  laws  of  descent,  we 
possess  simple  and  compendious  directions  for  repro- 
ducing in  thought  all  possible  motions  of  falling  bod- 
ies. A  formula  of  this  kind  is  a  complete  substitute 
for  a  full  table  of  motions  of  descent,  because  by  means 
of  the  formula  the  data  of  such  a  table  can  be  easily 
constructed  at  a  moment's  notice  without  the  least 
burdening  of  the  memory. 

No  human  mind  could  comprehend  all  the  individ- 
ual cases  of  refraction.  But  knowing  the  index  of  re- 
fraction for  the  two  media  presented,  and  the  familiar 
law  of  the  sines,  we  can  easily  reproduce  or  fill  out  in 
thought  every  conceivable  case  of  refraction.  The  ad- 
vantage here  consists  in  the  disburdening  of  the  mem- 
ory; an  end  immensely  furthered  by  the  written  preser- 
vation of  the  natural  constants.  More  than  this  com- 
prehensive and  condensed  report  about  facts  is  not 
contained  in  a  natural  law  of  this  sort.  In  reality,  the 
law  always  contains  less  than  the  fact  itself,  because  it 
does  not  reproduce  the  fact  as  a  whole  but  only  in 
that  aspect  of  it  which  is  important  for  us,  the  rest  be- 
ing either  intentionally  or  from  necessity  omitted. 
Natural  laws  may  be  likened  to  intellectual  type  of  a 


194        THE  ECONOMICAL  NATURE  OF  PHYSICS. 

higher  order,  partly  movable,  partly  stereotyped,  which 
last  on  new  editions  of  experience  may  become  down- 
right impediments. 

When  we  look  over  a  province  of  facts  for  the  first 
time,  it  appears  to  us  diversified,  irregular,  confused, 
full  of  contradictions.  We  first  succeed  in  grasping 
only  single  facts,  unrelated  with  the  others.  The 
province,  as  we  are  wont  to  say,  is  not  clear.  By  and 
by  we  discover  the  simple,  permanent  elements  of  the 
mosaic,  out  of  which  we  can  mentally  construct  the 
whole  province.  When  we  have  reached  a  point  where 
we  can  discover  everywhere  the  same  facts,  we  no 
longer  feel  lost  in  this  province ;  we  comprehend  it 
without  effort ;  it  is  explained  for  us. 

Let  me  illustrate  this  by  an  example.  As  soon  as 
we  have  grasped  the  fact  of  the  rectilinear  propagation 
of  light,  the  regular  course  of  our  thoughts  stumbles 
at  the  phenomena  of  refraction  and  diffraction.  As  soon 
as  we  have  cleared  matters  up  by  our  index  of  refrac- 
tion we  discover  that  a  special  index  is  necessary  for 
each  color.  Soon  after  we  have  accustomed  ourselves 
to  the  fact  that  light  added  to  light  increases  its  in- 
tensity, we  suddenly  come  across  a  case  of  total  dark- 
ness produced  by  this  cause.  Ultimately,  however, 
we  see  everywhere  in  the  overwhelming  multifarious- 
ness  of  optical  phenomena  the  fact  of  the  spatial  and 
temporal  periodicity  of  light,  with  its  velocity  of  propa- 
gation dependent  on  the  medium  and  the  period.  This 
tendency  of  obtaining  a  survey  of  a  given  province 


THE  ECONOMICAL  NATURE  OF  PHYSICS.       195 

with  the  least  expenditure  of  thought,  and  of  repre- 
senting all  its  facts  by  some  one  single  mental  process, 
may  be  justly  termed  an  economical  one. 

The  greatest  perfection  of  mental  economy  is  at- 
tained in  that  science  which  has  reached  the  highest 
formal  development,  and  which  is  widely  employed  in 
physical  inquiry,  namely,  in  mathematics.  Strange  as 
it  may  sound,  the  power  of  mathematics  rests  upon 
its  evasion  of  all  unnecessary  thought  and  on  its  won- 
derful saving  of  mental  operations.  Even  those  ar- 
rangement-signs which  we  call  numbers  are  a  system 
of  marvellous  simplicity  and  economy.  When  we  em- 
ploy the  multiplication-table  in  multiplying  numbers 
of  several  places,  and  so  use  the  results  of  old  opera- 
tions of  counting  instead  of  performing  the  whole  of 
each  operation  anew ;  when  we  consult  our  table  of 
logarithms,  replacing  and  saving  thus  new  calcula- 
tions by  old  ones  already  performed ;  when  we  employ 
determinants  instead  of  always  beginning  afresh  the 
solution  of  a  system  of  equations ;  when  we  resolve 
new  integral  expressions  into  familiar  old  integrals; 
we  see  in  this  simply  a  feeble  reflexion  of  the  intel- 
lectual activity  of  a  Lagrange  or  a  Cauchy,  who,  with 
the  keen  discernment  of  a  great  military  commander, 
substituted  for  new  operations  whole  hosts  of  old  ones. 
No  one  will  dispute  me  when  I  say  that  the  most  ele- 
mentary as  well  as  the  highest  mathematics  are  eco- 
nomically-ordered experiences  of  counting,  put  informs 
ready  for  use. 


ig6        THE  ECONOMICAL  NA  TURE  OF  PHYSICS. 

In  algebra  we  perform,  as  far  as  possible,  all  nu- 
merical operations  which  are  identical  in  form  once 
for  all,  so  that  only  a  remnant  of  work  is  left  for  the 
individual  case.  The  use  of  the  signs  of  algebra  and 
analysis,  which  are  merely  symbols  of  operations  to 
be  performed,  is  due  to  the  observation  that  we  can 
materially  disburden  the  mind  in  this  way  and  spare 
its  powers  for  more  important  and  more  difficult  du- 
ties, by  imposing  all  mechanical  operations  upon  the 
hand.  One  result  of  this  method,  which  attests  its 
economical  character,  is  the  construction  of  calculating 
machines.  The  mathematician  Babbage,  the  inventor 
of  the  difference-engine,  was  probably  the  first  who 
clearly  perceived  this  fact,  and  he  touched  upon  it, 
although  only  cursorily,  in  his  work,  The  Economy  of 
Manufactures  and  Machinery. 

The  student  of  mathematics  often  finds  it  hard  to 
throw  off  the  uncomfortable  feeling  that  his  science,  in 
the  person  of  his  pencil,  surpasses  him  in  intelligence, 
— an  impression  which  the  great  Euler  confessed  he 
often  could  not  get  rid  of.  This  feeling  finds  a  sort  of 
justification  when  we  reflect  that  the  majority  of  the 
ideas  we  deal  with  were  conceived  by  others,  often 
centuries  ago.  In  great  measure  it  is  really  the  intelli- 
gence of  other  people  that  confronts  us  in  science. 
The  moment  we  look  at  matters  in  this  light,  the  un- 
canniness  and  magical  character  of  our  impressions 
cease,  especially  when  we  remember  that  we  can  think 
over  again  at  will  any  one  of  those  alien  thoughts. 


THE  ECONOMICAL  NATURE  OF  PHYSICS.       197 

Physics  is  experience,  arranged  in  economical  or- 
der. By  this  order  not  only  is  a  broad  and  comprehen- 
sive view  of  what  we  have  rendered  possible,  but  also 
the  defects  and  the  needful  alterations  are  made  mani- 
fest, exactly  as  in  a  well-kept  household.  Physics 
shares  with  mathematics  the  advantages  of  succinct 
description  and  of  brief,  compendious  definition,  which 
precludes  confusion,  even  in  ideas  where,  with  no  ap- 
parent burdening  of  the  brain,  hosts  of  others  are  con- 
tained. Of  these  ideas  the  rich  contents  can  be  pro- 
duced at  any  moment  and  displayed  in  their  full  per- 
ceptual light.  Think  of  the  swarm  of  well-ordered  no- 
tions pent  up  in  the  idea  of  the  potential.  Is  it  wonder- 
ful that  ideas  containing  so  much  finished  labor  should 
be  easy  to  work  with? 

Our  first  knowledge,  thus,  is  a  product  of  the 
economy  of  self-preservation.  By  communication,  the 
experience  of  many  persons,  individually  acquired  at 
first,  is  collected  in  one.  The  communication  of 
knowledge  and  the  necessity  which  every  one  feels  of 
managing  his  stock  of  experience  with  the  least  expen- 
diture of  thought,  compel  us  to  put  our  knowledge  in 
economical  forms.  But  here  we  have  a  clue  which 
strips  science  of  all  its  mystery,  and  shows  us  what  its 
power  really  is.  With  respect  to  specific  results  it 
yields  us  nothing  that  we  could  not  reach  in  a  suffi- 
ciently long  time  without  methods.  There  is  no  prob- 
lem in  all  mathematics  that  cannot  be  solved  by  direct 
counting.  But  with  the  present  implements  of  mathe- 


I98       THE  ECONOMICAL  NATURE  OF  PHYSICS. 

matics  many  operations  of  counting  can  be  performed 
in  a  few  minutes  which  without  mathematical  methods 
would  take  a  lifetime.  Just  as  a  single  human  being, 
restricted  wholly  to  the  fruits  of  his  own  labor,  could 
never  amass  a  fortune,  but  on  the  contrary  the  accumu- 
lation of  the  labor  of  many  men  in  the  hands  of  one  is 
the  foundation  of  wealth  and  power,  so,  also,  no  knowl- 
edge worthy  of  the  name  can  be  gathered  up  in  a 
single  human  mind  limited  to  the  span  of  a  human  life 
and  gifted  only  with  finite  powers,  except  by  the  most 
exquisite  economy  of  thought  and  by  the  careful 
amassment  of  the  economically  ordered  experience  of 
thousands  of  co-workers.  What  strikes  us  here  as  the 
fruits  of  sorcery  are  simply  the  rewards  of  excellent 
housekeeping,  as  are  the  like  results  in  civil  life.  But 
the  business  of  science  has  this  advantage  over  every 
other  enterprise,  that  from  its  amassment  of  wealth  no 
one  suffers  the  least  loss.  This,  too,  is  its  blessing, 
its  freeing  and  saving  power. 

The  recognition  of  the  economical  character  of 
science  will  now  help  us,  perhaps,  to  understand  bet- 
ter certain  physical  notions. 

Those  elements  of  an  event  which  we  call  "cause 
and  effect  "  are  certain  salient  features  of  it,  which  are 
important  for  its  mental  reproduction.  Their  impor- 
tance wanes  and  the  attention  is  transferred  to  fresh 
characters  the  moment  the  event  or  experience  in 
question  becomes  familiar.  If  the  connexion  of  such 
features  strikes  us  as  a  necessary  one,  it  is  simply  be- 


THE  ECONOMICAL  NATURE  OF  PHYSICS. 


199 


cause  the  interpolation  of  certain  intermediate  links 
with  which  we  are  very  familiar,  and  which  possess, 
therefore,  higher  authority  for  us,  is  often  attended 
with  success  in  our  explanations.  That  ready  experience 
fixed  in  the  mosaic  of  the  mind  with  which  we  meet 
new  events,  Kant  calls  an  innate  concept  of  the  under- 
standing (  Verstandesbegriff}. 

The  grandest  principles  of  physics,  resolved  into 
their  elements,  differ  in  no  wise  from  the  descriptive 
principles  of  the  natural  historian.  The  question, 
"Why?"  which  is  always  appropriate  where  the  ex- 
planation of  a  contradiction  is  concerned,  like  all  proper 
habitudes  of  thought,  can  overreach  itself  and  be  asked 
where  nothing  remains  to  be  understood.  Suppose  we 
were  to  attribute  to  nature  the  property  of  producing 
like  effects  in  like  circumstances ;  just  these  like  cir- 
cumstances we  should  not  know  how  to  find.  Nature 
exists  once  only.  Our  schematic  mental  imitation  alone 
produces  like  events.  Only  in  the  mind,  therefore,  does 
the  mutual  dependence  of  certain  features  exist. 

All  our  efforts  to  mirror  the  world  in  thought  would 
be  futile  if  we  found  nothing  permanent  in  the  varied 
changes  of  things.  It  is  this  that  impels  us  to  form  the 
notion  of  substance,  the  source  of  which  is  not  differ- 
ent from  that  of  the  modern  ideas  relative  to  the  con- 
servation of  energy.  The  history  of  physics  furnishes 
numerous  examples  of  this  impulse  in  almost  all  fields, 
and  pretty  examples  of  it  may  be  traced  back  to  the 
nursery.  "  Where  does  the  light  go  to  when  it  is  put 


200        THE  ECONOMICAL  NATURE  OF  PHYSICS. 

out?  "  asks  the  child.  The  sudden  shrivelling  up  of  a 
hydrogen  balloon  is  inexplicable  to  a  child;  it  looks 
everywhere  for  the  large  body  which  was  just  there 
but  is  now  gone. 

Where  does  heat  come  from  ?  Where  does  heat 
go  to?  Such  childish  questions  in  the  mouths  of  ma- 
ture men  shape  the  character  of  a  century. 

In  mentally  separating  a  body  from  the  changeable 
environment  in  which  it  moves,  what  we  really  do 
is  to  extricate  a  group  of  sensations  on  which  our 
thoughts  are  fastened  and  which  is  of  relatively  greater 
stability  than  the  others,  from  the  stream  of  all  our 
sensations.  Absolutely  unalterable  this  group  is  not. 
Now  this,  now  that  member  of  it  appears  and  disap- 
pears, or  is  altered.  In  its  full  identity  it  never  re- 
curs. Yet  the  sum  of  its  constant  elements  as  compared 
with  the  sum  of  its  changeable  ones,  especially  if  we 
consider  the  continuous  character  of  the  transition,  is 
always  so  great  that  for  the  purpose  in  hand  the  former 
usually  appear  sufficient  to  determine  the  body's  iden- 
tity. But  because  we  can  separate  from  the  group 
every  single  member  without  the  body's  ceasing  to  be 
for  us  the  same,  we  are  easily  led  to  believe  that  after 
abstracting  all  the  members  something  additional 
would  remain.  It  thus  comes  to  pass  that  we  form 
the  notion  of  a  substance  distinct  from  its  attributes, 
of  a  thing-in-itself,  whilst  our  sensations  are  regarded 
merely  as  symbols  or  indications  of  the  properties  of 
this  thing-in-itself.  But  it  would  be  much  better  to 


THE  ECONOMICAL  NATURE  OF  PHYSICS.       201 

say  that  bodies  or  things  are  compendious  mental  sym- 
bols for  groups  of  sensations — symbols  that  do  not  ex- 
ist outside  of  thought.  Thus,  the  merchant  regards 
the  labels  of  his  boxes  merely  as  indexes  of  their  con- 
tents, and  not  the  contrary.  He  invests  their  con- 
tents, not  their  labels,  with  real  value.  The  same 
economy  which  induces  us  to  analyse  a  group  and  to 
establish  special  signs  for  its  component  parts,  parts 
which  also  go  to  make  up  other  groups,  may  likewise 
induce  us  to  mark  out  by  some  single  symbol  a  whole 
group. 

On  the  old  Egyptian  monuments  we  see  objects 
represented  which  do  not  reproduce  a  single  visual 
impression,  but  are  composed  of  various  impressions. 
The  heads  and  the  legs  of  the  figures  appear  in  pro- 
file, the  head-dress  and  the  breast  are  seen  from  the 
front,  and  so  on.  We  have  here,  so  to  speak,  a  mean 
view  of  the  objects,  in  forming  which  the  sculptor  has 
retained  what  he  deemed  essential,  and  neglected  what 
he  thought  indifferent.  We  have  living  exemplifica- 
tions of  the  processes  put  into  stone  on  the  walls  of 
these  old  temples,  in  the  drawings  of  our  children,  and 
we  also  observe  a  faithful  analogue  of  them  in  the  for- 
mation of  ideas  in  our  own  minds.  Only  in  virtue  of 
some  such  facility  of  view  as  that  indicated,  are  we 
allowed  to  speak  of  a  body.  When  we  speak  of  a  cube 
with  trimmed  corners — a  figure  which  is  not  a  cube — 
we  do  so  from  a  natural  instinct  of  economy,  which 
prefers  to  add  to  an  old  familiar  conception  a  correc- 


202        THE  ECONOMICAL  NA  TURE  OF  PHYSICS. 

tion  instead  of  forming  an  entirely  new  one.     This  is 
the  process  of  all  judgment. 

The  crude  notion  of  "body"  can  no  more  stand 
the  test  of  analysis  than  can  the  art  of  the  Egyptians 
or  that  of  our  little  children.  The  physicist  who  sees 
a  body  flexed,  stretched,  melted,  and  vaporised,  cuts 
up  this  body  into  smaller  permanent  parts ;  the  chem- 
ist splits  it  up  into  elements.  Yet  even  an  element  is 
not  unalterable.  Take  sodium.  When  warmed,  the 
white,  silvery  mass  becomes  a  liquid,  which,  when  the 
heat  is  increased  and  the  air  shut  out,  is  transformed 
into  a  violet  vapor,  and  on  the  heat  being  still  more 
increased  glows  with  a  yellow  light.  If  the  name  so- 
dium is  still  retained,  it  is  because  of  the  continuous 
character  of  the  transitions  and  from  a  necessary  in- 
stinct of  economy.  By  condensing  the  vapor,  the 
white  metal  may  be  made  to  reappear.  Indeed,  even 
after  the  metal  is  thrown  into  water  and  has  passed 
into  sodium  hydroxide,  the  vanished  properties  may 
by  skilful  treatment  still  be  made  to  appear ;  just  as  a 
moving  body  which  has  passed  behind  a  column  and 
is  lost  to  view  for  a  moment  may  make  its  appearance 
after  a  time.  It  is  unquestionably  very  convenient 
always  to  have  ready  the  name  and  thought  for  a 
group  of  properties  wherever  that  group  by  any  possi- 
bility can  appear.  But  more  than  a  compendious  eco- 
nomical symbol  for  these  phenomena,  that  name  and 
thought  is  not.  It  would  be  a  mere  empty  word  for 
one  in  whom  it  did  not  awaken  a  large  group  of  well- 


THE  ECONOMICAL  NATURE  OF  PHYSICS. 


203 


ordered  sense-impressions.  And  the  same  is  true  of 
the  molecules  and  atoms  into  which  the  chemical  ele- 
ment is  still  further  analysed. 

True,  it  is  customary  to  regard  the  conservation  of 
weight,  or,  more  precisely,  the  conservation  of  mass, 
as  a  direct  proof  of  the  constancy  of  matter.  But  this 
proof  is  dissolved,  when  we  go  to  the  bottom  of  it, 
into  such  a  multitude  of  instrumental  and  intellectual 
operations,  that  in  a  sense  it  will  be  found  to  consti- 
tute simply  an  equation  which  our  ideas  in  imitating 
facts  have  to  satisfy.  That  obscure,  mysterious  lump 
which  we  involuntarily  add  in  thought,  we  seek  for  in 
vain  outside  the  mind. 

It  is  always,  thus,  the  crude  notion  of  substance 
that  is  slipping  unnoticed  into  science,  proving  itself 
constantly  insufficient,  and  ever  under  the  necessity  of 
being  reduced  to  smaller  and  smaller  world-particles. 
Here,  as  elsewhere,  the  lower  stage  is  not  rendered 
indispensable  by  the  higher  which  is  built  upon  it,  no 
more  than  the  simplest  mode  of  locomotion,  walking, 
is  rendered  superfluous  by  the  most  elaborate  means  of 
transportation.  Body,  as  a  compound  of  light  and 
touch  sensations,  knit  together  by  sensations  of  space, 
must  be  as  familiar  to  the  physicist  who  seeks  it,  as  to 
the  animal  who  hunts  its  prey.  But  the  student  of  the 
theory  of  knowledge,  like  the  geologist  and  the  astron- 
omer, must  be  permitted  to  reason  back  from  the  forms 
which  are  created  before  his  eyes  to  others  which  he 
finds  ready  made  for  him. 


204       THE  ECONOMICAL  NATURE  Of*  PHYSICS. 

All  physical  ideas  and  principles  are  succinct  di- 
rections, frequently  involving  subordinate  directions, 
for  the  employment  of  economically  classified  expe- 
riences, ready  for  use.  Their  conciseness,  as  also  the 
fact  that  their  contents  are  rarely  exhibited  in  full, 
often  invests  them  with  the  semblance  of  independent 
existence.  Poetical  myths  regarding  such  ideas, — for 
example,  that  of  Time,  the  producer  and  devourer  of 
all  things, — do  not  concern  us  here.  We  need  only 
remind  the  reader  that  even  Newton  speaks  of  an  ab- 
solute time  independent  of  all  phenomena,  and  of  an 
absolute  space — views  which  even  Kant  did  not  shake 
off,  and  which  are  often  seriously  entertained  to-day. 
For  the  natural  inquirer,  determinations  of  time  are 
merely  abbreviated  statements  of  the  dependence  of 
one  event  upon  another,  and  nothing  more.  When 
we  say  the  acceleration  of  a  freely  falling  body  is  9  •  810 
metres  per  second,  we  mean  the  velocity  of  the  body 
with  respect  to  the  centre  of  the  earth  is  9-810  metres 
greater  when  the  earth  has  performed  an  additional 
86400th  part  of  its  rotation — a  fact  which  itself  can  be 
determined  only  by  the  earth's  relation  to  other  heav- 
enly bodies.  Again,  in  velocity  is  contained  simply  a 
relation  of  the  position  of  a  body  to  the  position  of 
the  earth.*  Instead  of  referring  events  to  the  earth 
we  may  refer  them  to  a  clock,  or  even  to  our  internal 
sensation  of  time.  Now,  because  all  are  connected, 


*It  is  clear  from  this  that  all  so-called  elementary  (differential)  laws  in- 
volve a  relation  to  the  Whole. 


THE  ECONOMICAL  NATURE  OF  PHYSICS.      ao5 

and  each  may  be  made  the  measure  of  the  rest,  the  il- 
lusion easily  arises  that  time  has  significance  inde- 
pendently of  all.  * 

The  aim  of  research  is  the  discovery  of  the  equa- 
tions which  subsist  between  the  elements  of  phenom- 
ena. The  equation  of  an  ellipse  expresses  the  universal 
conceivable  relation  between  its  co-ordinates,  of  which 
only  the  real  values  have  geometrical  significance. 
Similarly,  the  equations  between  the  elements  of  phe- 
nomena express  a  universal,  mathematically  conceiv- 
able relation.  Here,  however,  for  many  values  only 
certain  directions  of  change  are  physically  admissible. 
As  in  the  ellipse  only  certain  values  satisfying  the 
equation  are  realised,  so  in  the  physical  world  only 
certain  changes  of  value  occur.  Bodies  are  always  ac- 
celerated towards  the  earth.  Differences  of  tempera- 
ture, left  to  themselves,  always  grow  less  ;  and  so  on. 
Similarly,  with  respect  to  space,  mathematical  and 
physiological  researches  have  shown  that  the  space  of 
experience  is  simply  an  actual  case  of  many  conceiv- 
able cases,  about  whose  peculiar  properties  experience 
alone  can  instruct  us.  The  elucidation  which  this  idea 
diffuses  cannot  be  questioned,  despite  the  absurd  uses 
to  which  it  has  been  put. 

Let  us  endeavor  now  to  summarise  the  results  of 

*  If  it  be  objected,  that  in  the  case  of  perturbations  of  the  velocity  of  rota- 
tion of  the  earth,  we  could  be  sensible  of  such  perturbations,  and  being  obliged 
to  have  some  measure  of  time,  we  should  resort  to  the  period  of  vibration  of 
the  waves  of  sodium  light,— all  that  this  would  show  is  that  for  practical  rea- 
sons we  should  select  that  event  which  best  served  us  as  the  simfUit  common 
measure  of  the  others. 


206        THE  ECONOMICAL  NATURE  OF  PHYSICS. 

our  survey.  In  the  economical  schematism  of  science 
lie  both  its  strength  and  its  weakness.  Facts  are  al- 
ways represented  at  a  sacrifice  of  completeness  and 
never  with  greater  precision  than  fits  the  needs  of  the 
moment.  The  incongruence  between  thought  and  ex- 
perience, therefore,  will  continue  to  subsist  as  long  as 
the  two  pursue  their  course  side  by  side  ;  but  it  will 
be  continually  diminished. 

In  reality,  the  point  involved  is  always  the  com- 
pletion of  some  partial  experience ;  the  derivation  of 
one  portion  of  a  phenomenon  from  some  other.  In 
this  act  our  ideas  must  be  based  directly  upon  sensa- 
tions. We  call  this  measuring.*  The  condition  of 
science,  both  in  its  origin  and  in  its  application,  is  a 
great  relative  stability  of  our  environment.  What  it 
teaches  us  is  interdependence.  Absolute  forecasts, 
consequently,  have  no  significance  in  science.  With 
great  changes  in  celestial  space  we  should  lose  our 
co-ordinate  systems  of  space  and  time. 

When  a  geometer  wishes  to  understand  the  form  of 
a  curve,  he  first  resolves  it  into  small  rectilinear  ele- 
ments. In  doing  this,  however,  he  is  fully  aware  that 
these  elements  are  only  provisional  and  arbitrary  de- 
vices for  comprehending  in  parts  what  he  cannot  com- 
prehend as  a  whole.  When  the  law  of  the  curve  is 
found  he  no  longer  thinks  of  the  elements.  Similarly, 
it  would  not  become  physical  science  to  see  in  its  self- 


*  Measurement,  in  fact,  is  the  definition  of  one  phenomenon  by  another 
(standard)  phenomenon. 


THE  ECONOMICAL  NATURE  OF  PHYSICS.      207 

created,  changeable,  economical  tools,  molecules  and 
atoms,  realities  behind  phenomena,  forgetful  of  the 
lately  acquired  sapience  of  her  older  sister,  philosophy, 
in  substituting  a  mechanical  mythology  for  the  old 
animistic  or  metaphysical  scheme,  and  thus  creating 
no  end  of  suppositious  problems.  The  atom  must  re- 
main a  tool  for  representing  phenomena,  like  the 
functions  of  mathematics.  Gradually,  however,  as 
the  intellect,  by  contact  with  its  subject-matter,  grows 
in  discipline,  physical  science  will  give  up  its  mosaic 
play  with  stones  and  will  seek  out  the  boundaries  and 
forms  of  the  bed  in  which  the  living  stream  of  phe- 
nomena flows.  The  goal  which  it  has  set  itself  is  the 
simplest  and  most  economical  abstract  expression  of  facts. 

The  question  now  remains,  whether  the  same 
method  of  research  which  till  now  we  have  tacitly  re- 
stricted to  physics,  is  also  applicable  in  the  psychical 
domain.  This  question  will  appear  superfluous  to  the 
physical  inquirer.  Our  physical  and  psychical  views 
spring  in  exactly  the  same  manner  from  instinctive 
knowledge.  We  read  the  thoughts  of  men  in  their 
acts  and  facial  expressions  without  knowing  how. 
Just  as  we  predict  the  behavior  of  a  magnetic  needle 
placed  near  a  current  by  imagining  Ampere's  swim- 
mer in  the  current,  similarly  we  predict  in  thought  the 
acts  and  behavior  of  men  by  assuming  sensations,  feel- 
ings, and  wills  similar  to  our  own  connected  with  their 
bodies.  What  we  here  instinctively  perform  would 


208        THE  ECONOMICAL  NATURE  OF  PHYSICS. 

appear  to  us  as  one  of  the  subtlest  achievements  of 
science,  far  outstripping  in  significance  and  ingenuity 
Ampere's  rule  of  the  swimmer,  were  it  not  that  every 
child  unconsciously  accomplished  it.  The  question 
simply  is,  therefore,  to  grasp  scientifically,  that  is,  by 
conceptional  thought,  what  we  are  already  familiar 
with  from  other  sources.  And  here  much  is  to  be 
accomplished.  A  long  sequence  of  facts  is  to  be  dis- 
closed between  the  physics  of  expression  and  move- 
ment and  feeling  and  thought. 

We  hear  the  question,  "But  how  is  it  possible  to 
explain  feeling  by  the  motions  of  the  atoms  of  the 
brain  ?  "  Certainly  this  will  never  be  done,  no  more 
than  light  or  heat  will  ever  be  deduced  from  the  law 
of  refraction.  We  need  not  deplore,  therefore,  the 
lack  of  ingenious  solutions  of  this  question.  The  prob- 
lem is  not  a  problem.  A  child  looking  over  the  walls 
of  a  city  or  of  a  fort  into  the  moat  below  sees  with 
astonishment  living  people  in  it,  and  not  knowing  of 
the  portal  which  connects  the  wall  with  the  moat,  can- 
not understand  how  they  could  have  got  down  from 
the  high  ramparts.  So  it  is  with  the  notions  of  phys- 
ics. We  cannot  climb  up  into  the  province  of  psychol- 
ogy by  the  ladder  of  our  abstractions,  but  we  can  climb 
down  into  it. 

Let  us  look  at  the  matter  without  bias.  The  world 
consists  of  colors,  sounds,  temperatures,  pressures, 
spaces,  times,  and  so  forth,  which  now  we  shall  not 
call  sensations,  nor  phenomena,  because  in  either  term 


THE  ECONOMICAL  NATURE  OF  PHYSICS.      209 

an  arbitrary,  one-sided  theory  is  embodied,  but  simply 
elements.  The  fixing  of  the  flux  of  these  elements, 
whether  mediately  or  immediately,  is  the  real  object  of 
physical  research.  As  long  as,  neglecting  our  own 
body,  we  employ  ourselves  with  the  interdependence 
of  those  groups  of  elements  which,  including  men  and 
animals,  make  up  foreign  bodies,  we  are  physicists. 
For  example,  we  investigate  the  change  of  the  red 
color  of  a  body  as  produced  by  a  change  of  illumina- 
tion. But  the  moment  we  consider  the  special  in- 
fluence on  the  red  of  the  elements  constituting  our 
body,  outlined  by  the  well-known  perspective  with 
head  invisible,  we  are  at  work  in  the  domain  of  physi- 
ological psychology.  We  close  our  eyes,  and  the  red 
together  with  the  whole  visible  world  disappears. 
There  exists,  thus,  in  the  perspective  field  of  every  sense 
a  portion  which  exercises  on  all  the  rest  a  different 
and  more  powerful  influence  than  the  rest  upon  one 
another.  With  this,  however,  all  is  said.  In  the  light 
of  this  remark,  we  call  all  elements,  in  so  far  as  we  re- 
gard them  as  dependent  on  this  special  part  (our  body), 
sensations.  That  the  world  is  our  sensation,  in  this 
sense,  cannot  be  questioned.  But  to  make  a  system 
of  conduct  out  of  this  provisional  conception,  and  to 
abide  its  slaves,  is  as  unnecessary  for  us  as  would  be 
a  similar  course  for  a  mathematician  who,  in  varying  a 
series  of  variables  of  a  function  which  were  previously 
assumed  to  be  constant,  or  in  interchanging  the  inde- 


210        THE  ECONOMICAL  NATURE  OF  PHYSICS. 

pendent  variables,  finds  his  method  to  be  the  source 
of  some  very  surprising  ideas  for  him.* 

If  we  look  at  the  matter  in  this  unbiassed  light  it 
will  appear  indubitable  that  the  method  of  physiologi- 
cal psychology  is  none  other  than  that  of  physics; 
what  is  more,  that  this  science  is  a  part  of  physics. 
Its  subject-matter  is  not  different  from  that  of  phys- 
ics. It  will  unquestionably  determine  the  relations 
the  sensations  bear  to  the  physics  of  our  body.  We 
have  already  learned  from  a  member  of  this  academy 
(Hering)  that  in  all  probability  a  sixfold  manifoldness 
of  the  chemical  processes  of  the  visual  substance  cor- 
responds to  the  sixfold  manifoldness  of  color-sensation, 
and  a  threefold  manifoldness  of  the  physiological  pro- 
cesses to  the  threefold  manifoldness  of  space-sensa- 
tions. The  paths  of  reflex  actions  and  of  the  will  are 
followed  up  and  disclosed  ;  it  is  ascertained  what  re- 
gion of  the  brain  subserves  the  function  of  speech, 
what  region  the  function  of  locomotion,  etc.  That 
which  still  clings  to  our  body,  namely,  our  thoughts, 
will,  when  those  investigations  are  finished,  present  no 
difficulties  new  in  principle.  When  experience  has 
once  clearly  exhibited  these  facts  and  science  has 

*I  have  represented  the  point  of  view  here  taken  for  more  than  thirty 
years  and  developed  it  in  various  writings  (Erhaltung  der  Arbeit,  1872,  parts 
of  which  are  published  in  the  article  on  The  Conservation  of  Energy  in  this 
collection  ;  The  Forms  of  Liquids,  1872,  also  published  in  this  collection  ;  and 
the  Bewegungsempfindungen.  1875).  The  idea,  though  known  to  philosophers, 
is  unfamiliar  to  the  majority  of  physicists.  It  is  a  matter  of  deep  regret  to  me. 
therefore,  that  the  title  and  author  of  a  small  tract  which  accorded  with  my 
views  in  numerous  details  and  which  I  remember  having  caught  a  glance  of 
in  a  very  busy  period  (1879-1880),  have  so  completely  disappeared  from  my 
memory  that  all  efforts  to  obtain  a  clue  to  them  have  hitherto  been  fruitless. 


THE  ECONOMICAL  NATURE  OF  PHYSICS.       211 

marshalled  them  in  economic  and  perspicuous  order, 
there  is  no  doubt  that  we  shall  understand  them.  For 
other  "  understanding"  than  a  mental  mastery  of  facts 
never  existed.  Science  does  not  create  facts  from  facts, 
but  simply  orders  known  facts. 

Let  us  look,  now,  a  little  more  closely  into  the  modes 
of  research  of  physiological  psychology.  We  have  a 
very  clear  idea  of  how  a  body  moves  in  the  space  en- 
compassing it.  With  our  optical  field  of  sight  we  are 
very  familiar.  But  we  are  unable  to  state,  as  a  rule, 
how  we  have  come  by  an  idea,  from  what  corner  of 
our  intellectual  field  of  sight  it  has  entered,  or  by  what 
region  the  impulse  to  a  motion  is  sent  forth.  More- 
over, we  shall  never  get  acquainted  with  this  mental 
field  of  view  from  self-observation  alone.  Self-obser- 
vation, in  conjunction  with  physiological  research, 
which  seeks  out  physical  connexions,  can  put  this  field 
of  vision  in  a  clear  light  before  us,  and  will  thus  first 
really  reveal  to  us  our  inner  man. 

Primarily,  natural  science,  or  physics,  in  its  widest 
sense,  makes  us  acquainted  with  only  the  firmest  con- 
nexions of  groups  of  elements.  Provisorily,  we  may 
not  bestow  too  much  attention  on  the  single  constitu- 
ents of  those  groups,  if  we  are  desirous  of  retaining  a 
comprehensible  whole.  Instead  of  equations  between 
the  primitive  variables,  physics  gives  us,  as  much  the 
easiest  course,  equations  between  functions  of  those 
variables.  Physiological  psychology  teaches  us  how 
to  separate  the  visible,  the  tangible,  and  the  audible 


212        THE  ECONOMICAL  NATURE  OF  PHYSICS, 

from  bodies — a  labor  which  is  subsequently  richly  re- 
quited, as  the  division  of  the  subjects  of  physics  well 
shows.  Physiology  further  analyses  the  visible  into 
light  and  space  sensations ;  the  first  into  colors,  the 
last  also  into  their  component  parts  ;  it  resolves  noises 
into  sounds,  these  into  tones,  and  so  on.  Unquestion- 
ably this  analysis  can  be  carried  much  further  than  it 
has  been.  It  will  be  possible  in  the  end  to  exhibit  the 
common  elements  at  the  basis  of  very  abstract  but 
definite  logical  acts  of  like  form, — elements  which  the 
acute  jurist  and  mathematician,  as  it  were,  feels  out, 
with  absolute  certainty,  where  the  uninitiated  hears 
only  empty  words.  Physiology,  in  a  word,  will  reveal 
to  us  the  true  real  elements  of  the  world.  Physiological 
psychology  bears  to  physics  in  its  widest  sense  a  rela- 
tion similar  to  that  which  chemistry  bears  to  physics 
in  its  narrowest  sense.  But  far  greater  than  the  mu- 
tual support  of  physics  and  chemistry  will  be  that 
which  natural  science  and  psychology  will  render  each 
other.  And  the  results  that  shall  spring  from  this 
union  will,  in  all  likelihood,  far  outstrip  those  of  the 
modern  mechanical  physics. 

What  those  ideas  are  with  which  we  shall  compre- 
hend the  world  when  the  closed  circuit  of  physical  and 
psychological  facts  shall  lie  complete  before  us,  (that 
circuit  of  which  we  now  see  only  two  disjoined  parts,) 
cannot  be  foreseen  at  the  outset  of  the  work.  The 
men  will  be  found  who  will  see  what  is  right  and 
will  have  the  courage,  instead  of  wandering  in  the 


THE  ECONOMICAL  NATURE  OF  PHYSICS.      213 

intricate  paths  of  logical  and  historical  accident,  to 
enter  on  the  straight  ways  to  the  heights  from  which 
the  mighty  stream  of  facts  can  be  surveyed.  Whether 
the  notion  which  we  now  call  matter  will  continue  to 
have  a  scientific  significance  beyond  the  crude  pur- 
poses of  common  life,  we  do  not  know.  But  we  cer- 
tainly shall  wonder  how  colors  and  tones  which  were 
such  innermost  parts  of  us  could  suddenly  get  lost  in 
our  physical  world  of  atoms ;  how  we  could  be  sud- 
denly surprised  that  something  which  outside  us  sim- 
ply clicked  and  beat,  in  our  heads  should  make  light 
and  music ;  and  how  we  could  ask  whether  matter  can 
feel,  that  is  to  say,  whether  a  mental  symbol  for  a 
group  of  sensations  can  feel  ? 

We  cannot  mark  out  in  hard  and  fast  lines  the 
science  of  the  future,  but  we  can  foresee  that  the  rigid 
walls  which  now  divide  man  from  the  world  will  grad- 
ually disappear ;  that  human  beings  will  not  only  con- 
front each  other,  but  also  the  entire  organic  and  so- 
called  lifeless  world,  with  less  selfishness  and  with  live- 
lier sympathy.  Just  such  a  presentiment  as  this  per- 
haps possessed  the  great  Chinese  philosopher  Licius 
some  two  thousand  years  ago  when,  pointing  to  a  heap 
of  mouldering  human  bones,  he  said  to  his  scholars  in 
the  rigid,  lapidary  style  of  his  tongue :  "  These  and  I 
alone  have  the  knowledge  that  we  neither  live  nor  are 
dead." 


ON  TRANSFORMATION  AND  ADAPTA- 
TION IN  SCIENTIFIC  THOUGHT,* 


TT  was  towards  the  close  of  the  sixteenth  century 
-••  that  Galileo  with  a  superb  indifference  to  the  dia- 
lectic arts  and  sophistic  subtleties  of  the  Schoolmen  of 
his  time,  turned  the  attention  of  his  brilliant  mind 
to  nature.  By  nature  his  ideas  were  transformed  and 
released  from  the  fetters  of  inherited  prejudice.  At 
once  the  mighty  revolution  was  felt,  that  was  therewith 
effected  in  the  realm  of  human  thought — felt  indeed  in 
circles  far  remote  and  wholly  unrelated  to  the  sphere 
of  science,  felt  in  strata  of  society  that  hitherto  had 
only  indirectly  recognised  the  influence  of  scientific 
thought. 

*  Inaugural  Address,  delivered  on  assuming  the  Rectorate  of  the  Univer- 
sity of  Prague,  October  18,  1883. 

The  idea  presented  in  this  essay  is  neither  new  nor  remote.  I  have  touched 
upon  it  myself  on  several  occasions  (first  in  1867),  but  have  never  made  it  the 


and  the  newspapers,  I  have,  contrary  to  my  original  intention,  decided  to 
publish  it.  It  is  not  my  intention  to  trespass  here  upon  the  domain  of  biology. 
My  statements  are  to  be  taken  merely  as  the  expression  of  the  fact  that  no  one 
can  escape  the  influence  of  a  great  and  far-reaching  idea. 


ON  MENTAL  ADAPTATION.  215 

And  how  great  and  how  far-reaching  that  revolu- 
tion was  !  From  the  beginning  of  the  seventeenth  cen- 
tury till  its  close  we  see  arising,  at  least  in  embryo, 
almost  all  that  plays  a  part  in  the  natural  and  techni- 
cal science  of  to-da)',  almost  all  that  in  the  two  .cen- 
turies following  so  wonderfully  transformed  the  facial 
appearance  of  the  earth,  and  all  that  is  moving  onward 
in  process  of  such  mighty  evolution  to-day.  And  all 
this,  the  direct  result  of  Galilean  ideas,  the  direct  out- 
come of  that  freshly  awakened  sense  for  the  investiga- 
tion of  natural  phenomena  which  taught  the  Tuscan 
philosopher  to  form  the  concept  and  the  law  of  falling 
bodies  from  the  observation  of  a  falling  stone  !  Galileo 
began  his  investigations  without  an  implement  worthy 
of  the  name ;  he  measured  time  in  the  most  primitive 
way,  by  the  efflux  of  water.  Yet  soon  afterwards  the 
telescope,  the  microscope,  the  barometer,  the  ther- 
mometer, the  air-pump,  the  steam-engine,  the  pendu- 
lum, and  the  electrical  machine  were  invented  in  rapid 
succession.  The  fundamental  theorems  of  dynamical 
science,  of  optics,  of  heat,  and  of  electricity  were  all 
disclosed  in  the  century  that  followed  Galileo. 

Of  scarcely  less  importance,  it  seems,  was  that 
movement  which  was  prepared  for  by  the  illustrious 
biologists  of  the  hundred  years  just  past,  and  formally 
begun  by  the  late  Mr.  Darwin.  Galileo  quickened  the 
sense  for  the  simpler  phenomena  of  inorganic  nature. 
And  with  the  same  simplicity  and  frankness  that 
marked  the  efforts  of  Galileo,  and  without  the  aid  of 


216  ON  MENTAL  ADAPTATION. 

technical  or  scientific  instruments,  without  physical  or 
chemical  experiment,  but  solely  by  the  power  of 
thought  and  observation,  Darwin  grasps  a  new  prop- 
erty of  organic  nature — which  we  may  briefly  call  its 
plasticity*  With  the  same  directness  of  purpose,  Dar- 
win, too,  pursues  his  way.  With  the  same  candor 
and  love  of  truth,  he  points  out  the  strength  and  the 
weakness  of  his  demonstrations.  With  masterly  equa- 
nimity he  holds  aloof  from  the  discussion  of  irrelevant 
subjects  and  wins  alike  the  admiration  of  his  adherents 
and  of  his  adversaries. 

Scarcely  thirty  years  have  elapsedf  since  Darwin  first 
propounded  the  principles  of  his  theory  of  evolution. 

*At  first  sight  an  apparent  contradiction  arises  from  the  admission  of  both 
heredity  and  adaptation  ;  and  it  is  undoubtedly  true  that  a  strong  disposition 
to  heredity  precludes  great  capability  of  adaptation.  But  imagine  the  organ- 
ism to  be  a  plastic  mass  which  retains  the  form  transmitted  to  it  by  former 
influences  until  new  influences  modify  it ;  the  one  property  of  plasticity  will 
then  represent  capability  of  adaptation  as  well  as  power  of  heredity.  Analo- 
gous to  this  is  the  case  of  a  bar  of  magnetised  steel  of  high  coercive  force: 
the  steel  retains  its  magnetic  properties  until  a  new  force  displaces  them. 
Take  also  a  body  in  motion  :  the  body  retains  the  velocity  acquired  in  (inher- 
ited horn)  the  interval  of  time  just  preceding,  except  it  be  changed  in  the 
next  moment  by  an  accelerating  force.  In  the  case  of  the  body  in  motion  the 
change  of  velocity  (Abanderung)  was  looked  upon  as  a  matter  of  course,  while 
the  discovery  of  the  principle  of  inertia  (or  persistence)  created  surprise;  in 
Darwin's  case,  on  the  contrary,  heredity  (or  persistence)  was  taken  for  granted, 
while  the  principle  of  variation  (AbSnderung)  appeared  novel. 

Fully  adequate  views  are,  of  course,  to  be  reached  only  by  a  study  of  the 
original  facts  emphasised  by  Darwin,  and  not  by  these  analogies.  The  ex- 
ample referring  to  motion,  if  I  am  not  mistaken,  I  first  heard,  in  conversa- 
tion, from  my  friend  J.  Popper,  Esq.,  of  Vienna. 

Many  inquirers  look  upon  the  stability  of  the  species  as  something  settled, 
and  oppose  to  it  the  Darwinian  theory.  But  the  stability  of  the  species  is  it- 
self a  "theory."  The  essential  modifications  which  Darwin's  views  also  are 
undergoing  will  be  seen  from  the  works  of  Wallace  [and  Weismann],  but  more 
especially  from  a  book  of  W.  H.  Rolph,  Biologische  Probleme,  Leipsic,  1882. 
Unfortunately,  this  last  talented  investigator  is  no  longer  numbered  among 
the  living. 

T  Written  in  1883. 


ON  MENTAL  ADAPTATION.  217 

Yet,  already  we  see  his  ideas  firmly  rooted  in  every 
branch  of  human  thought,  however  remote.  Every- 
where, in  history,  in  philosophy,  even  in  the  physical 
sciences,  we  hear  the  watchwords :  heredity,  adapta- 
tion, selection.  We  speak  of  the  struggle  for  existence 
among  the  heavenly  bodies  and  of  the  struggle  for  ex- 
istence in  the  world  of  molecules.* 

The  impetus  given  by  Galileo  to  scientific  thought 
was  marked  in  every  direction ;  thus,  his  pupil,  Bo- 
relli,  founded  the  school  of  exact  medicine,  from 
whence  proceeded  even  distinguished  mathematicians. 
And  now  Darwinian  ideas,  in  the  same  way,  are  ani- 
mating all  provinces  of  research.  It  is  true,  nature  is 
not  made  up  of  two  distinct  parts,  the  inorganic  and 
the  organic ;  nor  must  these  two  divisions  be  treated 
perforce  by  totally  distinct  methods.  Many  sides,  how- 
ever, nature  has.  Nature  is  like  a  thread  in  an  intricate 
tangle,  which  must  be  followed  and  traced,  now  from 
this  point,  now  from  that.  But  we  must  never  imagine, 
— and  this  physicists  have  learned  from  Faraday  and 
J.  R.  Mayer, — that  progress  along  paths  once  entered 
upon  is  the  only  means  of  reaching  the  truth. 

It  will  devolve  upon  the  specialists  of  the  future  to 
determine  the  relative  tenability  and  fruitfulness  of  the 
Darwinian  ideas  in  the  different  provinces.  Here  I 
wish  simply  to  consider  the  growth  of  natural  knowl- 
edge in  the  light  of  the  theory  of  evolution.  For  knowl- 
edge, too,  is  a  product  of  organic  nature.  And  although 

*  See  Pfaundler,  Fogg.  Ann.,  Jubelband,  p.  182. 


2i8  ON  MENTAL  ADAPTATION. 

ideas,  as  such,  do  not  comport  themselves  in  all  respects 
like  independent  organic  individuals,  and  although 
violent  comparisons  should  be  avoided,  still,  if  Darwin 
reasoned  rightly,  the  general  imprint  of  evolution  and 
transformation  must  be  noticeable  in  ideas  also. 

I  shall  waive  here  the  consideration  of  the  fruitful 
topic  of  the  transmission  of  ideas  or  rather  of  the 
transmission  of  the  aptitude  for  certain  ideas.*  Nor 
would  it  come  within  my  province  to  discuss  psych- 
ical evolution  in  any  form,  as  Spencerf  and  many  other 
modern  psychologists  have  done,  with  varying  suc- 
cess. Neither  shall  I  enter  upon  a  discussion  of  the 
struggle  for  existence  and  of  natural  selection  among 
scientific  theories.  J  We  shall  consider  here  only  such 
processes  of  transformation  as  every  student  can  easily 
observe  in  his  own  mind. 

* 
*  * 

The  child  of  the  forest  picks  out  and  pursues  with 
marvellous  acuteness  the  trails  of  animals.  He  out- 
wits and  overreaches  his  foes  with  surpassing  cunning. 
He  is  perfectly  at  home  in  the  sphere  of  his  peculiar 
experience.  But  confront  him  with  an  unwonted  phe- 
nomenon ;  place  him  face  to  face  with  a  technical  pro- 
duct of  modern  civilisation,  and  he  will  lapse  into  im- 
potency  and  helplessness.  Here  are  facts  which  he 

*  See  the  beautiful  discussions  of  this  point  in  Bering's  Memory  as  a  Gen- 
eral Function  of  Organised  Matter  (1870),  Chicago,  The  Open  Court  Publishing 
Co.,  1887.  Compare  also  Dubois,  Ueber  die  Uebung,  Berlin,  1881. 

t  Spencer,  The  Principles  of  Psychology.     London,  1872. 

J  See  the  article  The  Velocity  of  Light,  page  63. 


ON  MENTAL  ADAPTATION.  2ig 

does  not  comprehend.  If  he  endeavors  to  grasp  their 
meaning,  he  misinterprets  them.  He  fancies  the  moon, 
when  eclipsed,  to  be  tormented  by  an  evil  spirit.  To 
his  mind  a  puffing  locomotive  is  a  living  monster.  The 
letter  accompanying  a  commission  with  which  he  is 
entrusted,  having  once  revealed  his  thievishness,  is  in 
his  imagination  a  conscious  being,  which  he  must  hide 
beneath  a  stone,  before  venturing  to  commit  a  fresh 
trespass.  Arithmetic  to  him  is  like  the  art  of  the 
geomancers  in  the  Arabian  Nights, — an  art  which  is 
able  to  accomplish  every  imaginable  impossibility. 
And,  like  Voltaire's  ingenu,  when  placed  in  our  social 
world,  he  plays,  as  we  think,  the  maddest  pranks. 

With  the  man  who  has  made  the  achievements  of 
modern  science  and  civilisation  his  own,  the  case  is 
quite  different.  He  sees  the  moon  pass  temporarily 
into  the  shadow  of  the  earth.  He  feels  in  his  thoughts 
the  water  growing  hot  in  the  boiler  of  the  locomotive ; 
he  feels  also  the  increase  of  the  tension  which  pushes 
the  piston  forward.  Where  he  is  not  able  to  trace  the 
direct  relation  of  things  he  has  recourse  to  his  yard- 
stick and  table  of  logarithms,  which  aid  and  facilitate 
his  thought  without  predominating  over  it.  Such  opin- 
ions as  he  cannot  concur  in,  are  at  least  known  to  him, 
and  he  knows  how  to  meet  them  in  argument. 

Now,  wherein  does  the  difference  between  these 
two  men  consist?  The  train  of  thought  habitually 
employed  by  the  first  one  does  not  correspond  to  the 
facts  that  he  sees.  He  is  surprised  and  nonplussed 


220  ON  MENTAL  ADAPTA  TION. 

at  every  step.  But  the  thoughts  of  the  second  man 
follow  and  anticipate  events,  his  thoughts  have  be- 
come adapted  or  accommodated  to  the  larger  field  of 
observation  and  activity  in  which  he  is  located  ;  he  con- 
ceives things  as  they  are.  The  Indian's  sphere  of  ex- 
perience, however,  is  quite  different ;  his  bodily  organs 
of  sense  are  in  constant  activity;  he  is  ever  intensely 
alert  and  on  the  watch  for  his  foes  ;  or,  his  entire  at- 
tention and  energy  are  engaged  in  procuring  suste- 
nance. Now,  how  can  such  a  creature  project  his  mind 
into  futurity,  foresee  or  prophesy?  This  is  not  possi- 
ble until  our  fellow-beings  have,  in  a  measure,  relieved 
us  of  our  concern  for  existence.  It  is  then  that  we 
acquire  freedom  for  observation,  and  not  infrequently 
too  that  narrowness  of  thought  which  society  helps  and 
teaches  us  to  disregard. 

If  we  move  for  a  time  within  a  fixed  circle  of  phe- 
nomena which  recur  with  unvarying  uniformity,  our 
thoughts  gradually  adapt  themselves  to  our  environ- 
ment ;  our  ideas  reflect  unconsciously  our  surround- 
ings. The  stone  we  hold  in  our  hand,  when  dropped, 
not  only  falls  to  the  ground  in  reality ;  it  also  falls  in 
our  thoughts.  Iron-filings  dart  towards  a  magnet  in 
imagination  as  well  as  in  fact,  and,  when  thrown  into 
a  fire,  they  grew  hot  in  conception  as  well. 

The  impulse  to  complete  mentally  a  phenomenon 
that  has  been  only  partially  observed,  has  not  its  origin 
in  the  phenomenon  itself;  of  this  fact,  we  are  fully 
sensible.  And  we  well  know  that  it  does  not  lie  within 


ON  MENTAL  ADAPTATION,  221 

the  sphere  of  our  volition.  It  seems  to  confront  us 
rather  as  a  power  and  a  law  imposed  from  without 
and  controlling  both  thought  and  facts. 

The  fact  that  we  are  able  by  the  help  of  this  law  to 
prophesy  and  forecast,  merely  proves  a  sameness  or 
uniformity  of  environment  sufficient  to  effect  a  men- 
tal adaptation  of  this  kind.  A  necessity  of  fulfilment, 
however,  is  not  contained  in  this  compulsory  principle 
which  controls  our  thoughts ;  nor  is  it  in  any  way  de- 
termined by  the  possibility  of  prediction.  We  are  al- 
ways obliged,  in  fact,  to  await  the  completion  of  what 
has  been  predicted.  Errors  and  departures  are  con- 
stantly discernible,  and  are  slight  only  in  provinces  of 
great  rigid  constancy,  as  in  astronomy. 

In  cases  where  our  thoughts  follow  the  connexion 
of  events  with  ease,  and  in  instances  where  we  posi- 
tively forefeel  the  course  of  a  phenomenon,  it  is  nat- 
ural to  fancy  that  the  latter  is  determined  by  and  must 
conform  to  our  thoughts.  But  the  belief  in  that  mys- 
terious agency  called  causality ',  which  holds  thought  and 
event  in  unison,  is  violently  shaken  when  a  person  first 
enters  a  province  of  inquiry  in  which  he  has  previously 
had  no  experience.  Take  for  instance  the  strange 
interaction  of  electric  currents  and  magnets,  or  the 
reciprocal  action  of  currents,  which  seem  to  defy  all 
the  resources  of  mechanical  science.  Let  him  be  con- 
fronted with  such  phenomena  and  he  will  immediately 
feel  himself  forsaken  by  his  power  of  prediction ;  he 
will  bring  nothing  with  him  into  this  strange  field  of 


222  ON  MENTAL  ADAPTATION. 

events  but  the  hope  of  soon  being  able  to  adapt  his 
ideas  to  the  new  conditions  there  presented. 

A  person  constructs  from  a  bone  the  remaining 
anatomy  of  an  animal ;  or  from  the  visible  part  of  a 
half-concealed  wing  of  a  butterfly  he  infers  and  recon- 
structs the  part  concealed.  He  does  so  with  a  feeling 
of  highest  confidence  in  the  accuracy  of  his  results ; 
and  in  these  processes  we  find  nothing  preternatural 
or  transcendent.  But  when  physicists  adapt  their 
thoughts  to  conform  to  the  dynamical  course  of  events 
in  time,  we  invariably  surround  their  investigations 
with  a  metaphysical  halo ;  yet  these  latter  adaptations 
bear  quite  the  same  character  as  the  former,  and  our 
only  reason  for  investing  them  with  a  metaphysical 
garb,  perhaps,  is  their  high  practical  value.* 

Let  us  consider  for  a  moment  what  takes  place 
when  the  field  of  observation  to  which  our  ideas  have 
been  adapted  and  now  conform,  becomes  enlarged. 
We  had,  let  us  say,  always  seen  heavy  bodies  sink 
when  their  support  was  taken  away;  we  had  also  seen, 
perhaps,  that  the  sinking  of  heavier  bodies  forced 
lighter  bodies  upwards.  But  now  we  see  a  lever  in 
action,  and  we  are  suddenly  struck  with  the  fact  that 
a  lighter  body  is  lifting  another  of  much  greater  weight. 

*  I  am  well  aware  that  the  endeavor  to  confine  oneself  in  natural  research 
to  facts  is  often  censured  as  an  exaggerated  fear  of  metaphysical  spooks. 
But  I  would  observe,  that,  judged  by  the  mischief  which  they  have  wrought, 
the  metaphysical,  of  all  spooks,  are  the  least  fabulous.  It  is  not  to  be  denied 
that  many  forms  of  thought  were  not  originally  acquired  by  the  individual,  but 
were  antecedently  formed,  or  rather  prepared  for,  in  the  development  of  the 
species,  in  some  such  way  as  Spencer,  Haeckel,  Hering,  and  others  have 
supposed,  and  as  I  myself  have  hinted  on  various  occasions. 


ON  MENTAL  ADAPTATION.  223 

Our  customary  train  of  thought  demands  its  rights; 
the  new  and  unwonted  event  likewise  demands  its 
rights.  From  this  conflict  between  thought  and  fact 
the  problem  arises ;  out  of  this  partial  contrariety  springs 
the  question,  "Why?"  With  the  new  adaptation  to  the 
enlarged  field  of  observation,  the  problem  disappears, 
or,  in  other  words,  is  solved.  In  the  instance  cited, 
we  must  adopt  the  habit  of  always  considering  the 
mechanical  work  performed. 

The  child  just  awakening  into  consciousness  of  the 
world,  knows  no  problem.  The  bright  flower,  the 
ringing  bell,  are  all  new  to  it ;  yet  it  is  surprised  at 
nothing.  The  out  and  out  Philistine,  whose  only 
thoughts  lie  in  the  beaten  path  of  his  every-day  pur- 
suits, likewise  has  no  problems.  Everything  goes  its 
wonted  course,  and  if  perchance  a  thing  go  wrong  at 
times,  it  is  at  most  a  mere  object  of  curiosity  and 
not  worth  serious  consideration.  In  fact,  the  question 
"Why?  "loses  all  warrant  in  relations  where  we  are 
familiar  with  every  aspect  of  events.  But  the  capable 
and  talented  young  man  has  his  head  full  of  problems ; 
he  has  acquired,  to  a  greater  or  less  degree,  certain 
habitudes  of  thought,  and  at  the  same  time  he  is  con- 
stantly observing  what  is  new  and  unwonted,  and  in 
his  case  there  is  no  end  to  the  questions,  "Why?" 

Thus,  the  factor  which  most  promotes  scientific 
thought  is  the  gradual  widening  of  the  field  of  expe- 
rience. We  scarcely  notice  events  we  are  accustomed 
to ;  the  latter  do  not  really  develop  their  intellectual 


224  ON  MENTAL  ADAPTA  TJON. 

significance  until  placed  in  contrast  with  something  to 
which  we  are  unaccustomed.  Things  that  at  home 
are  passed  by  unnoticed,  delight  us  when  abroad, 
though  they  may  appear  in  only  slightly  different  forms. 
The  sun  shines  with  heightened  radiance,  the  flowers 
bloom  in  brighter  colors,  our  fellow-men  accost  us 
with  lighter  and  happier  looks.  And,  returning  home, 
we  find  even  the  old  familiar  scenes  more  inspiring 
and  suggestive  than  before. 

Every  motive  that  prompts  and  stimulates  us  to 
modify  and  transform  our  thoughts,  proceeds  from 
what  is  new,  uncommon,  and  not  understood.  Novelty 
excites  wonder  in  persons  whose  fixed  habits  of  thought 
are  shaken  and  disarranged  by  what  they  see.  But  the 
element  of  wonder  never  lies  in  the  phenomenon  or 
event  observed ;  its  place  is  in  the  person  observing. 
People  of  more  vigorous  mental  type  aim  at  once  at  an 
adaptation  of  thought  that  will  conform  to  what  they 
have  observed.  Thus  does  science  eventually  become 
the  natural  foe  of  the  wonderful.  The  sources  of  the 
marvellous  are  unveiled,  and  surprise  gives  way  to 
calm  interpretation. 

Let  us  consider  such  a  mental  transformative  pro- 
cess in  detail.  The  circumstance  that  heavy  bodies 
fall  to  the  earth  appears  perfectly  natural  and  regular. 
But  when  a  person  observes  that  wood  floats  upon 
water,  and  that  flames  and  smoke  rise  in  the  air,  then 
the  contrary  of  the  first  phenomenon  is  presented. 
An  olden  theory  endeavors  to  explain  these  facts  by  im- 


ON  MENTAL  ADAPTA  TION.  225 

puting  to  substances  the  power  of  volition,  as  that  at- 
tribute which  is  most  familiar  to  man.  It  asserted 
that  every  substance  seeks  its  proper  place,  heavy 
bodies  tending  downwards  and  light  ones  upwards. 
It  soon  turned  out,  however,  that  even  smoke  had 
weight,  that  it,  too,  sought  its  place  below,  and  that 
it  was  forced  upwards  only  because  of  the  downward 
tendency  of  the  air,  as  wood  is  forced  to  the  surface  of 
water  because  the  water  exerts  the  greater  downward 
pressure. 

Again,  we  see  a  body  thrown  into  the  air.  It  ascends. 
How  is  it  that  it  does  not  seek  its  proper  place?  Why 
does  the  velocity  of  its  "violent"  motion  decrease  as 
it  rises,  while  that  of  its  "natural"  fall  increases  as  it 
descends.  If  we  mark  closely  the  relation  between 
these  two  facts,  the  problem  will  solve  itself.  We  shall 
see,  as  Galileo  did,  that  the  decrease  of  velocity  in 
rising  and  the  increase  of  velocity  in  falling  are  one 
and  the  same  phenomenon,  viz.,  an  increase  of  velo- 
city towards  the  earth.  Accordingly,  it  is  not  a  place 
that  is  assigned  to  the  body,  but  an  increase  of  velo- 
city towards  the  earth. 

By  this  idea  the  movements  of  heavy  bodies  are 
rendered  perfectly  familiar.  Newton,  now,  firmly 
grasping  this  new  way  of  thinking,  sees  the  moon  and 
the  planets  moving  in  their  paths  upon  principles  sim- 
ilar to  those  which  determine  the  motion  of  a  projec- 
tile thrown  into  the  air.  Yet  the  movements  of  the 
planets  were  marked  by  peculiarities  which  compelled 


226  ON  MENTAL  ADAPTATION. 

him  once  more  to  modify  slightly  his  customary  mode 
of  thought.  The  heavenly  bodies,  or  rather  the  parts 
composing  them,  do  not  move  with  constant  accelera- 
tions towards  each  other,  but  "attract  each  other," 
directly  as  the  mass  and  inversely  as  the  square  of  the 
distance. 

This  latter  notion,  which  includes  the  one  applying 
to  terrestrial  bodies  as  a  special  case,  is,  as  we  see, 
quite  different  from  the  conception  from  which  we 
started.  How  limited  in  scope  was  the  original  idea 
and  to  what  a  multitude  of  phenomena  is  not  the  pres- 
ent one  applicable  !  Yet  there  is  a  trace,  after  all, 
of  the  "search  for  place"  in  the  expression  "attrac- 
tion." And  it  would  be  folly,  indeed,  for  us  to  avoid, 
with  punctilious  dread,  this  conception  of  "  attraction" 
as  bearing  marks  of  its  pedigree.  It  is  the  historical 
base  of  the  Newtonian  conception  and  it  still  continues 
to  direct  our  thoughts  in  the  paths  so  long  familiar  to 
us.  Thus,  the  happiest  ideas  do  not  fall  from  heaven, 
but  spring  from  notions  already  existing. 

Similarly,  a  ray  of  light  was  first  regarded  as  a  con- 
tinuous and  homogeneous  straight  line.  It  then  be- 
came the  path  of  projection  for  minute  missiles;  then 
an  aggregate  of  the  paths  of  countless  different  kinds 
of  missiles.  It  became  periodic  ;  it  acquired  various 
sides ;  and  ultimately  it  even  lost  its  motion  in  a 
straight  line. 

The  electric  current  was  conceived  originally  as 
the  flow  of  a  hypothetical  fluid.  To  this  conception 


ON  MENTAL  ADAPTATION.  227 

was  soon  added  the  notion  of  a  chemical  current,  the 
notion  of  an  electric,  magnetic,  and  anisotropic  optical 
field,  intimately  connected  with  the  path  of  the  cur- 
rent. And  the  richer  a  conception  becomes  in  follow- 
ing and  keeping  pace  with  facts,  the  better  adapted  it 
is  to  anticipate  them. 

Adaptive  processes  of  this  kind  have  no  assignable 
beginning,  inasmuch  as  every  problem  that  incites 
to  new  adaptation,  presupposes  a  fixed  habitude  of 
thought.  Moreover,  they  have  no  visible  end  ;  in  so 
far  as  experience  never  ceases.  Science,  accordingly, 
stands  midway  in  the  evolutionary  process ;  and  science 
may  advantageously  direct  and  promote  this  process, 
but  it  can  never  take  its  place.  That  science  is  incon- 
ceivable the  principles  of  which  would  enable  a  person 
with  no  experience  to  construct  the  world  of  experi- 
ence, without  a  knowledge  of  it.  One  might  just  as 
well  expect  to  become  a  great  musician,  solely  by  the 
aid  of  theory,  and  without  musical  experience ;  or  to 
become  a  painter  by  following  the  directions  of  a  text- 
book. 

In  glancing  over  the  history  of  an  idea  with  which 
we  have  become  perfectly  familiar,  we  are  no  longer 
able  to  appreciate  the  full  significance  of  its  growth. 
The  deep  and  vital  changes  that  have  been  effected  in 
the  course  of  its  evolution,  are  recognisable  only  from 
the  astounding  narrowness  of  view  with  which  great 
contemporary  scientists  have  occasionally  opposed 
each  other.  Huygens's  wave-theory  of  light  was  in- 


228  ON  MENTAL  ADAPTA  TION, 

comprehensible  to  Newton,  and  Newton's  idea  of  uni- 
versal gravity  was  unintelligible  to  Huygens.  But  a 
century  afterwards  both  notions  were  reconcilable, 
even  in  ordinary  minds. 

On  the  other  hand,  the  original  creations  of  pio- 
neer intellects,  unconsciously  formed,  do  not  assume 
a  foreign  garb ;  their  form  is  their  own.  In  them, 
childlike  simplicity  is  joined  to  the  maturity  of  man- 
hood, and  they  are  not  to  be  compared  with  processes 
of  thought  in  the  average  mind.  The  latter  are  carried 
on  as  are  the  acts  of  persons  in  the  state  of  mesmerism, 
where  actions  involuntarily  follow  the  images  which 
the  words  of  other  persons  suggest  to  their  minds. 

The  ideas  that  have  become  most  familiar  through 
long  experience,  are  the  very  ones  that  intrude  them- 
selves into  the  conception  of  every  new  fact  observed. 
In  every  instance,  thus,  they  become  involved  in  a 
struggle  for  self-preservation,  and  it  is  just  they  that 
are  seized  by  the  inevitable  process  of  transformation. 

Upon  this  process  rests  substantially  the  method 
of  explaining  by  hypothesis  new  and  uncomprehended 
phenomena.  Thus,  instead  of  forming  entirely  new 
notions  to  explain  the  movements  of  the  heavenly 
bodies  and  the  phenomena  of  the  tides,  we  imagine  the 
material  particles  composing  the  bodies  of  the  universe 
to  possess  weight  or  gravity  with  respect  to  one  an- 
other. Similarly,  we  imagine  electrified  bodies  to  be 
freighted  with  fluids  that  attract  and  repel,  or  we  con- 
ceive the  space  between  them  to  be  in  a  state  of  elas- 


ON  MENTAL  ADAPTATION.  229 

tic  tension.  In  so  doing,  we  substitute  for  new  ideas 
distinct  and  more  familiar  notions  of  old  experience- 
notions  which  to  a  great  extent  run  unimpeded  in  their 
courses,  although  they  too  must  suffer  partial  trans- 
formation. 

The  animal  cannot  construct  new  members  to  per- 
form every  new  function  that  circumstances  and  fate 
demand  of  it.  On  the  contrary  it  is  obliged  to  make 
use  of  those  it  already  possesses.  When  a  vertebrate 
animal  chances  into  an  environment  where  it  must 
learn  to  fly  or  swim,  an  additional  pair  of  extremities  is 
not  grown  for  the  purpose.  On  the  contrary,  the  ani- 
mal must  adapt  and  transform  a  pair  that  it  already 
has. 

The  construction  of  hypotheses,  therefore,  is  not 
the  product  of  artificial  scientific  methods.  This  pro- 
cess is  unconsciously  carried  on  in  the  very  infancy  of 
science.  Even  later,  hypotheses  do  not  become  det- 
rimental and  dangerous  to  progress  except  when  more 
reliance  is  placed  on  them  than  on  the  facts  them- 
selves; when  the  contents  of  the  former  are  more 
highly  valued  than  the  latter,  and  when,  rigidly  ad- 
hering to  hypothetical  notions,  we  overestimate  the 
ideas  we  possess  as  compared  with  those  we  have  to 
acquire. 

The  extension  of  our  sphere  of  experience  always 
involves  a  transformation  of  our  ideas.  It  matters  not 
whether  the  face  of  nature  becomes  actually  altered, 
presenting  new  and  strange  phenomena,  or  whether 


230  ON  MENTAL  ADAPTATION. 

these  phenomena  are  brought  to  light  by  an  intentional 
or  accidental  turn  of  observation.  In  fact,  all  the  va- 
ried methods  of  scientific  inquiry  and  of  purposive 
mental  adaptation  enumerated  by  John  Stuart  Mill, 
those  of  observation  as  well  as  those  of  experiment, 
are  ultimately  recognisable  as  forms  of  one  fundamen- 
tal method,  the  method  of  change,  or  variation.  It  is 
through  change  of  circumstances  that  the  natural  phi- 
losopher learns.  This  process,  however,  is  by  no  means 
confined  to  the  investigator  of  nature.  The  historian, 
the  philosopher,  the  jurist,  the  mathematician,  the 
artist,  the  aesthetician,*  all  illuminate  and  unfold  their 
ideas  by  producing  from  the  rich  treasures  of  memory 
similar,  but  different,  cases ;  thus,  they  observe  and 
experiment  in  their  thoughts.  Even  if  all  sense-expe- 
rience should  suddenly  cease,  the  events  of  the  days 
past  would  meet  in  different  attitudes  in  the  mind 
and  the  process  of  adaptation  would  still  continue — a 
process  which,  in  contradistinction  to  the  adaptation 
of  thoughts  to  facts  in  practical  spheres,  would  be 
strictly  theoretical,  being  an  adaptation  of  thoughts  to 
thoughts. 

The  method  of  change  or  variation  brings  before  us 
like  cases  of  phenomena,  having  partly  the  same  and 
partly  different  elements.  It  is  only  by  comparing 
different  cases  of  refracted  light  at  changing  angles  of 
incidence  that  the  common  factor,  the  constancy  of 

*  Compare,  for  example,  Schiller,  Zerstreute  Betrachtungen  fiber  verschie- 
dene  dsthetische  Gegenstande, 


ON  MENTAL  ADAPTATION,  231 

the  refractive  index,  is  disclosed.  And  only  by  com- 
paring the  refractions  of  light  of  different  colors,  does 
the  difference,  the  inequality  of  the  indices  of  refrac- 
tion, arrest  the  attention.  Comparison  based  upon 
change  leads  the  mind  simultaneously  to  the  highest 
abstractions  and  to  the  finest  distinctions. 

Undoubtedly,  the  animal  also  is  able  to  distinguish 
between  the  similar  and  dissimilar  of  two  cases.  Its 
consciousness  is  aroused  by  a  noise  or  a  rustling,  and 
its  motor  centre  is  put  in  readiness.  The  sight  of  the 
creature  causing  the  disturbance,  will,  according  to  its 
size,  provoke  flight  or  prompt  pursuit;  and  in  the  lat- 
ter case,  the  more  exact  distinctions  will  determine  the 
mode  of  attack.  But  man  alone  attains  to  the  faculty 
of  voluntary  and  conscious  comparison.  Man  alone 
can,  by  his  power  of  abstraction,  rise,  in  one  moment, 
to  the  comprehension  of  principles  like  the  conserva- 
tion of  mass  or  the  conservation  of  energy,  and  in  the 
next  observe  and  mark  the  arrangement  of  the  iron 
lines  in  the  spectrum.  In  thus  dealing  with  the  ob- 
jects of  his  conceptual  life,  his  ideas  unfold  and  ex- 
pand, like  his  nervous  system,  into  a  widely  ramified 
and  organically  articulated  tree,  on  which  he  may  fol- 
low every  limb  to  its  farthermost  branches,  and,  when 
occasion  demands,  return  to  the  trunk  from  which  he 
started. 

The  English  philosopher  Whewell  has  remarked 
that  two  things  are  requisite  to  the  formation  of  sci- 
ence :  facts  and  ideas.  Ideas  alone  lead  to  empty 


232  ON  MENTAL  ADAPTATION. 

speculation ;  mere  facts  can  yield  no  organic  knowl- 
edge. We  see  that  all  depends  upon  the  capacity  of 
adapting  existing  notions  to  fresh  facts. 

Over-readiness  to  yield  to  every  new  fact  prevents 
fixed  habits  of  thought  from  arising.  Excessively  rigid 
habits  of  thought  impede  freedom  of  observation.  In 
the  struggle,  in  the  compromise  between  judgment 
and  prejudgment  (prejudice),  if  we  may  use  the  term, 
our  understanding  of  things  broadens. 

Habitual  judgment,  applied  to  a  new  case  without 
antecedent  tests,  we  call  prejudgment  or  prejudice. 
Who  does  not  know  its  terrible  power !  But  we  think 
less  often  of  the  importance  and  utility  of  prejudice. 
Physically,  no  one  could  exist,  if  he  had  to  guide  and 
regulate  the  circulation,  respiration,  and  digestion  of 
his  body  by  conscious  and  purposive  acts.  So,  too, 
no  one  could  exist  intellectually  if  he  had  to  form  judg- 
ments on  every  passing  experience,  instead  of  allow- 
ing himself  to  be  controlled  by  the  judgments  he  has 
already  formed.  Prejudice  is  a  sort  of  reflex  motion 
in  the  province  of  intelligence. 

On  prejudices,  that  is,  on  habitual  judgments  not 
tested  in  every  case  to  which  they  are  applied,  reposes 
a  goodly  portion  of  the  thought  and  work  of  the  natu- 
ral scientist.  On  prejudices  reposes  most  of  the  con- 
duct of  society.  With  the  sudden  disappearance  of 
prejudice  society  would  hopelessly  dissolve.  That 
prince  displayed  a  deep  insight  into  the  power  of  in- 
tellectual habit,  who  quelled  the  loud  menaces  and 


ON  MENTAL  ADAPTATION.  233 

demands  of  his  body-guard  for  arrears  of  pay  and  com- 
pelled them  to  turn  about  and  march,  by  simply  pro- 
nouncing the  regular  word  of  command  ;  he  well  knew 
that  they  would  be  unable  to  resist  that. 

Not  until  the  discrepancy  between  habitual  judg- 
ments and  facts  becomes  great  is  the  investigator  im- 
plicated in  appreciable  illusion.  Then  tragic  compli- 
cations and  catastrophes  occur  in  the  practical  life  of 
individuals  and  nations — crises  where  man,  placing 
custom  above  life,  instead  of  pressing  it  into  the  ser- 
vice of  life,  becomes  the  victim  of  his  error.  The  very 
power  which  in  intellectual  life  advances,  fosters,  and 
sustains  us,  may  in  other  circumstances  delude  and 

destroy  us. 

* 
*  * 

Ideas  are  not  all  of  life.  They  are  only  momentary 
efflorescences  of  light,  designed  to  illuminate  the  paths 
of  the  will.  But  as  delicate  reagents  on  our  organic 
evolution  our  ideas  are  of  paramount  importance.  No 
theory  can  gainsay  the  vital  transformation  which  we 
feel  taking  place  within  us  through  their  agency.  Nor 
is  it  necessary  that  we  should  have  a  proof  of  this  pro- 
cess. We  are  immediately  assured  of  it. 

The  transformation  of  ideas  thus  appears  as  a  part 
of  the  general  evolution  of  life,  as  a  part  of  its  adap- 
tation to  a  constantly  widening  sphere  of  action.  A 
granite  boulder  on  a  mountain-side  tends  towards  the 
earth  below.  It  must  abide  in  its  resting-place  for 
thousands  of  years  before  its  support  gives  way.  The 


234  ON  MENTAL  ADAPTATION. 

shrub  that  grows  at  its  base  is  farther  advanced  ;  it 
accommodates  itself  to  summer  and  winter.  The  fox 
which,  overcoming  the  force  of  gravity,  creeps  to  the 
summit  where  he  has  scented  his  prey,  is  freer  in  his 
movements  than  either.  The  arm  of  man  reaches 
further  still ;  and  scarcely  anything  of  note  happens 
in  Africa  or  Asia  that  does  not  leave  an  imprint  upon 
his  life.  What  an  immense  portion  of  the  life  of 
other  men  is  reflected  in  ourselves ;  their  joys,  their 
affections,  their  happiness  and  misery  !  And  this  too, 
when  we  survey  only  our  immediate  surroundings, 
and  confine  our  attention  to  modern  literature.  How 
much  more  do  we  experience  when  we  travel  through 
ancient  Egypt  with  Herodotus,  when  we  stroll  through 
the  streets  of  Pompeii,  when  we  carry  ourselves  back 
to  the  gloomy  period  of  the  crusades  or  to  the  golden 
age  of  Italian  art,  now  making  the  acquaintance  of  a 
physician  of  Moliere,  and  now  that  of  a  Diderot  or  of 
a  D'Alembert.  What  a  great  part  of  the  life  of  others, 
of  their  character  and  their  purpose,  do  we  not  absorb 
through  poetry  and  music  !  And  although  they  only 
gently  touch  the  chords  of  our  emotions,  like  the  mem- 
ory of  youth  softly  breathing  upon  the  spirit  of  an 
aged  man,  we  have  nevertheless  lived  them  over  again 
in  part.  How  great  and  comprehensive  does  self  be- 
come in  this  conception  ;  and  how  insignificant  the 
person  !  Egoistical  systems  both  of  optimism  and  pes- 
simism perish  with  their  narrow  standard  of  the  im- 
port of  intellectual  life.  We  feel  that  the  real  pearls 


ON  MENTAL  ADAPTA  TION~,  235 

of  life  lie  in  the  ever  changing  contents  of  conscious- 
ness, and  that  the  person  is  merely  an  indifferent  sym- 
bolical thread  on  which  they  are  strung.* 

We  are  prepared,  thus,  to  regard  ourselves  and 
every  one  of  our  ideas  as  a  product  and  a  subject  of 
universal  evolution  ;  and  in  this  way  we  shall  advance 
sturdily  and  unimpeded  along  the  paths  which  the 
future  will  throw  open  to  us.f 

*We  must  not  be  deceived  in  imagining  that  the  happiness  of  other  peo- 
ple is  not  a  very  considerable  and  essential  portion  of  our  own.  It  is  common 
capital,  which  cannot  be  created  by  the  individual,  and  which  does  not  perish 
with  him.  The  formal  and  material  limitation  of  the  ego  is  necessary  and  suf- 
ficient only  for  the  crudest  practical  objects,  and  cannot  subsist  in  a  broad  con- 
ception. Humanity  in  its  entirety  may  be  likened  to  a  polyp-plant.  The 
material  and  organic  bonds  of  individual  union  have,  indeed,  been  severed  ; 
they  would  only  have  impeded  freedom  of  movement  and  evolution.  But  the 
ultimate  aim,  the  psychical  connexion  of  the  whole,  has  been  attained  in  a 
much  higher  degree  through  the  richer  development  thus  made  possible. 

tC.  E.  von  Baer,  the  subsequent  opponent  of  Darwin  and  Haeckel,  has 
discussed  in  two  beautiful  addresses  (Das  allgemeinste  Gesetz  der  Natur  in 
aller  Entwickelung,  and  Welche  Auffassung  der  lebenden  Natur  ist  die  rich- 
tige,  und  wie  ist  diese  Auffassung  auf  die  Entomologie  anzuwnden .')  the 
narrowness  of  the  view  which  regards  an  animal  in  its  existing  state  as 
finished  and  complete,  instead  of  conceiving  it  as  a  phase  in  the  series  of  evo- 
lutionary forms  and  regarding  the  species  itself  as  a  phase  of  the  development 
of  the  animal  world  in  general. 


ON  THE  PRINCIPLE  OF  COMPARISON 
IN  PHYSICS.* 


^WENTY  years  ago  when  Kirchhoff  defined  the  ob- 
-*-  ject  of  mechanics  as  the  "description,  in  complete 
and  very  simple  terms,  of  the  motions  occurring  in  na- 
ture," he  produced  by  the  statement  a  peculiar  impres- 
sion. Fourteen  years  subsequently,  Boltzmann,  in  the 
life-like  picture  which  he  drew  of  the  great  inquirer, 
could  still  speak  of  the  universal  astonishment  at  this 
novel  method  of  treating  mechanics,  and  we  meet  with 
epistemological  treatises  to-day,  which  plainly  show 
how  difficult  is  the  acceptance  of  this  point  of  view.  A 
modest  and  small  band  of  inquirers  there  were,  how- 
ever, to  whom  Kirchhoff's  few  words  were  tidings  of  a 
welcome  and  powerful  ally  in  the  epistemological  field. 
Now,  how  does  it  happen  that  we  yield  our  assent 
so  reluctantly  to  the  philosophical  opinion  of  an  in- 
quirer for  whose  scientific  achievements  we  have  only 
words  of  praise  ?  One  reason  probably  is  that  few  in- 
quirers can  find  time  and  leisure,  amid  the  exacting 

*An  address  delivered  before  the  General  Session  of  the  German  Associa- 
tion of  Naturalists  and  Physicians,  at  Vienna,  Sept.  24,  1894. 


ON  COMPARISON  IN  PHYSICS.  237 

employments  demanded  for  the  acquisition  of  new 
knowledge,  to  inquire  closely  into  that  tremendous 
psychical  process  by  which  science  is  formed.  Further, 
if  is  inevitable  that  much  should  be  put  into  Kirchhoff's 
rigid  words  that  they  were  not  originally  intended  to 
convey,  and  that  much  should  be  found  wanting  in 
them  that  had  always  been  regarded  as  an  essential 
element  of  scientific  knowledge.  What  can  mere  de- 
scription accomplish  ?  What  has  become  of  explana- 
tion, of  our  insight  into  the  causal  connexion  of  things  ? 

* 
*  * 

Permit  me,  for  a  moment,  to  contemplate  not  the 
results  of  science,  but  the  mode  of  its  growth,  in  a 
frank  and  unbiassed  manner.  We  know  of  only  one 
source  of  immediate  revelation  of  scientific  facts — our 
senses.  Restricted  to  this  source  alone,  thrown  wholly 
upon  his  own  resources,  obliged  to  start  always  anew, 
what  could  the  isolated  individual  accomplish  ?  Of  a 
stock  of  knowledge  so  acquired  the  science  of  a  dis- 
tant negro  hamlet  in  darkest  Africa  could  hardly  give 
us  a  sufficiently  humiliating  conception.  For  there 
that  veritable  miracle  of  thought-transference  has  al- 
ready begun  its  work,  compared  with  which  the  mir- 
acles of  the  spiritualists  are  rank  monstrosities — com- 
munication by  language*  Reflect,  too,  that  by  means 
of  the  magical  characters  which  our  libraries  contain 
we  can  raise  the  spirits  of  the  "the  sovereign  dead  of 
old  "  from  Faraday  to  Galileo  and  Archimedes,  through 
ages  of  time — spirits  who  do  not  dismiss  us  with  am- 


*38  ON  COMPARISON  IN  PHYSICS. 

biguous  and  derisive  oracles,  but  tell  us  the  best  they 
know;  then  shall  we  feel  what  a  stupendous  and  in- 
dispensable factor  in  the  formation  of  science  com- 
munication is.  Not  the  dim,  half-conscious  surmises 
of  the  acute  observer  of  nature  or  critic  of  humanity 
belong  to  science,  but  only  that  which  they  possess 
clearly  enough  to  communicate  to  others. 

But  how,  now,  do  we  go  about  this  communication 
of  a  newly  acquired  experience,  of  a  newly  observed 
fact?  As  the  different  calls  and  battle-cries  of  gre- 
garious animals  are  unconsciously  formed  signs  for 
a  common  observation  or  action,  irrespective  of  the 
causes  which  produce  such  action — a  fact  that  already 
involves  the  germ  of  the  concept ;  so  also  the  words 
of  human  language,  which  is  only  more  highly  spe- 
cialised, are  names  or  signs  for  universally  known 
facts,  which  all  can  observe  or  have  observed.  If  the 
mental  representation,  accordingly,  follows  the  new 
fact  at  once  and  passively,  then  that  new  fact  must,  of 
itself,  immediately  be  constituted  and  represented  in 
thought  by  facts  already  universally  known  and  com- 
monly observed.  Memory  is  always  ready  to  put  for- 
ward for  comparison  known  facts  which  resemble  the 
new  event,  or  agree  with  it  in  certain  features,  and 
so  renders  possible  that  elementary  internal  judgment 
which  the  mature  and  definitively  formulated  judgment 
soon  follows. 

Comparison,  as  the  fundamental  condition  of  com- 
munication, is  the  most  powerful  inner  vital  element 


ON  COMPARISON  IN  PHYSICS.  239 

of  science.  The  zoologist  sees  in  the  bones  of  the 
wing-membranes  of  bats,  fingers;  he  compares  the 
bones  of  the  cranium  with  the  vertebrae,  the  embryos 
of  different  organisms  with  one  another,  and  the  dif- 
ferent stages  of  development  of  the  same  organism 
with  one  another.  The  geographer  sees  in  Lake  Garda 
a  fjord,  in  the  Sea  of  Aral  a  lake  in  process  of  drying 
up.  The  philologist  compares  different  languages  with 
one  another,  and  the  formations  of  the  same  language 
as  well.  If  it  is  not  customary  to  speak  of  compara- 
tive physics  in  the  same  sense  that  we  speak  of  com- 
parative anatomy,  the  reason  is  that  in  a  science  of 
such  great  experimental  activity  the  attention  is  turned 
away  too  much  from  the  contemplative  element.  But 
like  all  other  sciences,  physics  lives  and  grows  by 

comparison. 

* 
*  * 

The  manner  in  which  the  result  of  the  comparison 
finds  expression  in  the  communication,  varies  of  course 
very  much.  When  we  say  that  the  colors  of  the  spec- 
trum are  red,  yellow,  green,  blue,  and  violet,  the  des- 
ignations employed  may  possibly  have  been  derived 
from  the  technology  of  tattooing,  or  they  may  subse- 
quently have  acquired  the  significance  of  standing  for 
the  colors  of  the  rose,  the  lemon,  the  leaf,  the  corn- 
flower, and  the  violet.  From  the  frequent  repetition 
of  such  comparisons,  however,  made  under  the  most 
manifold  circumstances,  the  inconstant  features,  as 
compared  with  the  permanent  congruent  features,  get 


24o  ON  COMPARISON-  IN  PHVSICS. 

so  obliterated  that  the  latter  acquire  a  fixed  significance 
independent  of  every  object  and  connexion,  or  take  on 
as  we  say  an  abstract  or  conceptual  import.  No  one 
thinks  at  the  word  "  red  "  of  any  other  agreement  with 
the  rose  than  that  of  color,  or  at  the  word  "  straight" 
of  any  other  property  of  a  stretched  cord  than  the 
sameness  of  direction.  Just  so,  too,  numbers,  orig- 
inally the  names  of  the  fingers  of  the  hands  and  feet, 
from  being  used  as  arrangement-signs  for  all  kinds  of 
objects,  were  lifted  to  the  plane  of  abstract  concepts. 
A  verbal  report  (communication)  of  a  fact  that  uses 
only  these  purely  abstract  implements,  we  call  a  direct 
description. 

The  direct  description  of  a  fact  of  any  great  ex- 
tent is  an  irksome  task,  even  where  the  requisite  no- 
tions are  already  completely  developed.  What  a  sim- 
plification it  involves  if  we  can  say,  the  fact  A  now 
considered  comports  itself,  not  in  one,  but  in  many  or 
in  all  its  features,  like  an  old  and  well-known  fact  B. 
The  moon  comports  itself  as  a  heavy  body  does  with 
respect  to  the  earth  ;  light  like  a  wave-motion  or  an 
electric  vibration ;  a  magnet,  as  if  it  were  laden  with 
gravitating  fluids,  and  so  on.  We  call  such  a  descrip- 
tion, in  which  we  appeal,  as  it  were,  to  a  description 
already  and  elsewhere  formulated,  or  perhaps  still  to 
be  precisely  formulated,  an  indirect  description.  We 
are  at  liberty  to  supplement  this  description,  gradually, 
by  direct  description,  to  correct  it,  or  to  replace  it  alto- 
gether. We  see,  thus,  without  difficulty,  that  what  is 


ON  COMPARISON  IN  PHYSICS.  241 

called  a  theory  or  a  theoretical  idea,  falls  under  the 
category  of  what  is  here  termed  indirect  description. 

* 
*  * 

What,  now,  is  a  theoretical  idea  ?  Whence  do  we 
get  it  ?  What  does  it  accomplish  for  us  ?  Why  does  it 
occupy  a  higher  place  in  our  judgment  than  the  mere 
holding  fast  to  a  fact  or  an  observation  ?  Here,  too, 
memory  and  comparison  alone  are  in  play.  But  in- 
stead of  a  single  feature  of  resemblance  culled  from 
memory,  in  this  case  a  great  system  of  resemblances 
confronts  us,  a  well-known  physiognomy,  by  means  of 
which  the  new  fact  is  immediately  transformed  into  an 
old  acquaintance.  Besides,  it  is  in  the  power  of  the 
idea  to  offer  us  more  than  we  actually  see  in  the  new 
fact,  at  the  first  moment ;  it  can  extend  the  fact,  and 
enrich  it  with  features  which  we  are  first  induced  to 
seek  from  such  suggestions,  and  which  are  often  ac- 
tually found.  It  is  this  rapidity  in  extending  knowl- 
edge that  gives  to  theory  a  preference  over  simple  ob- 
servation. But  that  preference  is  wholly  quantitative. 
Qualitatively,  and  in  real  essential  points,  theory  dif- 
fers from  observation  neither  in  the  mode  of  its  origin 
nor  in  its  last  results. 

The  adoption  of  a  theory,  however,  always  involves 
a  danger.  For  a  theory  puts  in  the  place  of  a  fact  A 
in  thought,  always  a  different,  but  simpler  and  more 
familiar  fact  B,  which  in  some  relations  can  mentally 
represent  A,  but  for  the  very  reason  that  it  is  differ- 
ent, in  other  relations  cannot  represent  it.  If  now,  as 


242  ON  COMPARISON  IN  PHYSICS. 

may  readily  happen,  sufficient  care  is  not  exercised, 
the  most  fruitful  theory  ntay,  in  special  circumstances, 
become  a  downright  obstacle  to  inquiry.  Thus,  the 
emission-theory  of  light,  in  accustoming  the  physicist 
to  think  of  the  projectile  path  of  the  "light-particles" 
as  an  undifferentiated  straight-line,  demonstrably  im- 
peded the  discovery  of  the  periodicity  of  light.  By 
putting  in  the  place  of  light  the  more  familiar  phe- 
nomena of  sound,  Huygens  renders  light  in  many  of 
its  features  a  familiar  event,  but  with  respect  to  polari- 
sation, which  lacks  the  longitudinal  waves  with  which 
alone  he  was  acquainted,  it  had  for  him  a  doubly 
strange  aspect.  He  is  unable  thus  to  grasp  in  abstract 
thought  the  fact  of  polarisation,  which  is  before  his 
eyes,  whilst  Newton,  merely  by  adapting  to  the  obser- 
vation his  thoughts,  and  putting  this  question,  "An- 
nan radiorum  luminis  diversa  sunt  latera  ? ' '  abstractly 
grasped  polarisation,  that  is,  directly  described  it,  a 
century  before  Malus.  On  the  other  hand,  if  the 
agreement  of  the  fact  with  the  idea  theoretically  repre- 
senting it,  extends  further  than  its  inventor  originally 
anticipated,  then  we  may  be  led  by  it  to  unexpected 
discoveries,  of  which  conical  refraction,  circular  po- 
larisation by  total  reflexion,  Hertz's  waves  offer  ready 
examples,  in  contrast  to  the  illustrations  given  above. 
Our  insight  into  the  conditions  indicated  will  be 
improved,  perhaps,  by  contemplating  the  development 
of  some  theory  or  other  more  in  detail.  Let  us  con- 
sider a  magnetised  bar  of  steel  by  the  side  of  a  second 


ON  COMPARISON  IN  PHYSICS.  243 

unmagnetised  bar,  in  all  other  respects  the  same.  The 
second  bar  gives  no  indication  of  the  presence  of  iron- 
filings  ;  the  first  attracts  them.  Also,  when  the  iron- 
filings  are  absent,  we  must  think  of  the  magnetised 
bar  as  in  a  different  condition  from  that  of  the  unmag- 
netised. For,  that  the  mere  presence  of  the  iron-filings 
does  not  induce  the  phenomenon  of  attraction  is  proved 
by  the  second  unmagnetised  bar.  The  ingenuous  man, 
who  finds  in  his  will,  as  his  most  familiar  source  of 
power,  the  best  facilities  for  comparison,  conceives  a 
species  of  spirit  in  the  magnet.  The  behavior  of  a 
warm  body  or  of  an  electrified  body  suggests  similar 
ideas.  This  is  the  point  of  view  of  the  oldest  theory, 
fetishism,  which  the  inquirers  of  the  early  Middle 
Ages  had  not  yet  overcome,  and  which  in  its  last  ves- 
tiges, in  the  conception  of  forces,  still  flourishes  in 
modern  physics.  We  see,  thus,  the  dramatic  element 
need  no  more  be  absent  in  a  scientific  description,  than 
in  a  thrilling  novel. 

If,  on  subsequent  examination,  it  be  observed  that 
a  cold  body,  in  contact  with  a  hot  body,  warms  itself, 
so  to  speak,  at  the  expense  of  the  hot  body;  further, 
that  when  the  substances  are  the  same,  the  cold  body, 
which,  let  us  say,  has  twice  the  mass  of  the  other, 
gains  only  half  the  number  of  degrees  of  temperature 
that  the  other  loses,  a  wholly  new  impression  arises. 
The  demoniac  character  of  the  event  vanishes,  for  the 
supposed  spirit  acts  not  by  caprice,  but  according  to 
fixed  laws.  In  its  place,  however,  instinctively  the 


244  ON  COMPARISON  IN  PHYSICS. 

notion  of  a  substance  is  substituted,  part  of  which  flows 
over  from  the  one  body  to  the  other,  but  the  total 
amount  of  which,  representable  by  the  sum  of  the  pro- 
ducts of  the  masses  into  the  respective  changes  of 
temperature,  remains  constant.  Black  was  the  first  to 
be  powerfully  struck  with  this  resemblance  of  thermal 
processes  to  the  motion  of  a  substance,  and  under  its 
guidance  discovered  the  specific  heat,  the  heat  of  fu- 
sion, and  the  heat  of  vaporisation  of  bodies.  Gaining 
strength  and  fixity,  however,  from  these  successes, 
this  notion  of  substance  subsequently  stood  in  the  way 
of  scientific  advancement.  It  blinded  the  eyes  of  the 
successors  of  Black,  and  prevented  them  from  seeing 
the  manifest  fact,  which  every  savage  knows,  that  heat 
is  produced  by  friction.  Fruitful  as  that  notion  was 
for  Black,  helpful  as  it  still  is  to  the  learner  to-day  in 
Black's  special  field,  permanent  and  universal  validity 
as  a  theory  it  could  never  maintain.  But  what  is  essen- 
tial, conceptually,  in  it,  viz.,  the  constancy  of  the  pro- 
duct-sum above  mentioned,  retains  its  value  and  may 
be  regarded  as  a  direct  description  of  Black's  facts. 

It  stands  to  reason  that  those  theories  which  push 
themselves  forward  unsought,  instinctively,  and  wholly 
of  their  own  accord,  should  have  the  greatest  power, 
should  carry  our  thoughts  most  with  them,  and  exhibit 
the  staunchest  powers  of  self-preservation.  On  the 
other  hand,  it  may  also  be  observed  that  when  criti- 
cally scrutinised  such  theories  are  extremely  apt  to 
lose  their  cogency.  We  are  constantly  busied  with 


ON  COMPARISON  IN  PHYSICS.  245 

"substance,"  its  modes  of  action  have  stamped  them- 
selves indelibly  upon  our  thoughts,  our  vividest  and 
clearest  reminiscences  are  associated  with  it.  It  should 
cause  us  no  surprise,  therefore,  that  Robert  Mayer  and 
Joule,  who  gave  the  final  blow  to  Black's  substantial 
conception  of  heat,  should  have  re-introduced  the 
same  notion  of  substance  in  a  more  abstract  and  mod- 
ified form,  only  applying  to  a  much  more  extensive 
field. 

Here,  too,  the  psychological  circumstances  which 
impart  to  the  new  conception  its  power,  lie  clearly  be- 
fore us.  By  the  unusual  redness  of  the  venous  blood 
in  tropical  climates  Mayer's  attention  is  directed  to 
the  lessened  expenditure  of  internal  heat  and  to  the 
proportionately  lessened  consumption  of  material  by  the 
human  body  in  those  climates.  But  as  every  effort  of 
the  human  organism,  including  its  mechanical  work, 
is  connected  with  the  consumption  of  material,  and  as 
work  by  friction  can  engender  heat,  therefore  heat  and 
work  appear  in  kind  equivalent,  and  between  them  a 
proportional  relation  must  subsist.  Not  every  quantity, 
but  the  appropriately  calculated  sum  of  the  two,  as 
connected  with  a  proportionate  consumption  of  mate- 
rial, appears  substantial. 

By  exactly  similar  considerations,  relative  to  the 
economy  of  the  galvanic  element,  Joule  arrived  at  his 
view  \  he  found  experimentally  that  the  sum  of  the 
heat  evolved  in  the  circuit,  of  the  heat  consumed  in  the 
combustion  of  the  gas  developed,  of  the  electro-mag- 


246  ON  COMPARISON  IN  PHYSICS. 

netic  work  of  the  current,  properly  calculated,  —  in 
short,  the  sum  of  all  the  effects  of  the  battery, — is  con- 
nected with  a  proportionate  consumption  of  zinc.  Ac- 
cordingly, this  sum  itself  has  a  substantial  character. 
Mayer  was  so  absorbed  with  the  view  attained, 
that  the  indestructibility  of  force,  in  our  phraseology 
work,  appeared  to  him  a  priori  evident.  "The  crea- 
tion or  annihilation  of  a  force,"  he  says,  "lies  with- 
out the  province  of  human  thought  and  power."  Joule 
expressed  himself  to  a  similar  effect :  "  It  is  manifestly 
absurd  to  suppose  that  the  powers  with  which  God 
has  endowed  matter  can  be  destroyed."  Strange  to 
say,  on  the  basis  of  such  utterances,  not  Joule,  but 
Mayer,  was  stamped  as  a  metaphysician.  We  may 
be  sure,  however,  that  both  men  were  merely  giving 
expression,  and  that  half-unconsciously,  to  a  powerful 
formal  need  of  the  new  simple  view,  and  that  both 
would  have  been  extremely  surprised  if  it  had  been 
proposed  to  them  that  their  principle  should  be  sub- 
mitted to  a  philosophical  congress  or  ecclesiastical 
synod  for  a  decision  upon  its  validity.  But  with  all 
agreements,  the  attitude  of  these  two  men,  in  other 
respects,  was  totally  different.  Whilst  Mayer  repre- 
sented this  formal  need  with  all  the  stupendous  in- 
stinctive force  of  genius,  we  might  say  almost  with  the 
ardor  of  fanaticism,  yet  was  withal  not  wanting  in  the 
conceptive  ability  to  compute,  prior  to  all  other  in- 
quirers, the  mechanical  equivalent  of  heat  from  old 
physical  constants  long  known  and  at  the  disposal  of 


ON  COMPARISON  IN  PHYSICS.  247 

all,  and  so  to  set  up  for  the  new  doctrine  a  programme 
embracing  all  physics  and  physiology ;  Joule,  on  the 
other  hand,  applied  himself  to  the  exact  verification  of 
the  doctrine  by  beautifully  conceived  and  masterfully 
executed  experiments,  extending  over  all  departments 
of  physics.  Soon  Helmholtz  too  attacked  the  problem, 
in  a  totally  independent  and  characteristic  manner. 
After  the  professional  virtuosity  with  which  this  phys- 
icist grasped  and  disposed  of  all  the  points  unsettled 
by  Mayer's  programme  and  more  besides,  what  espe- 
cially strikes  us  is  the  consummate  critical  lucidity  of 
this  young  man  of  twenty-six  years.  In  his  exposition 
is  wanting  that  vehemence  and  impetuosity  which 
marked  Mayer's.  The  principle  of  the  conservation 
of  energy  is  no  self-evident  or  a  priori  proposition  for 
him.  What  follows,  on  the  assumption  that  that  prop- 
osition obtains  ?  In  this  hypothetical  form,  he  subju- 
gates his  matter. 

I  must  confess,  I  have  always  marvelled  at  the 
aesthetic  and  ethical  taste  of  many  of  our  contempo- 
raries who  have  managed  to  fabricate  out  of  this  rela- 
tion of  things,  odious  national  and  personal  questions, 
instead  of  praising  the  good  fortune  that  made  several 
such  men  work  together  and  of  rejoicing  at  the  in- 
structive diversity  and  idiosyncrasies  of  great  minds 
fraught  with  such  rich  consequences  for  us. 

We  know  that  still  another  theoretical  conception 
played  a  part  in  the  development  of  the  principle  of 
energy,  which  Mayer  held  aloof  from,  namely,  the  con- 


248  ON  COMPARISON  IN  PHYSICS. 

ception  that  heat,  as  also  the  other  physical  processes, 
are  due  to  motion.  But  once  the  principle  of  energy 
has  been  reached,  these  auxiliary  and  transitional  the- 
ories discharge  no  essential  function,  and  we  may  re- 
gard the  principle,  like  that  which  Black  gave,  as  a 
contribution  to  the  direct  description  of  a  widely  ex- 
tended domain  of  facts. 

It  would  appear  from  such  considerations  not  only 
advisable,  but  even  necessary,  with  all  due  recogni- 
tion of  the  helpfulness  of  theoretic  ideas  in  research, 
yet  gradually,  as  the  new  facts  grow  familiar,  to  sub- 
stitute for  indirect  description  direct  description,  which 
contains  nothing  that  is  unessential  and  restricts  itself 
absolutely  to  the  abstract  apprehension  of  facts.  We 
might  almost  say,  that  the  descriptive  sciences,  so 
called  with  a  tincture  of  condescension,  have,  in  re- 
spect of  scientific  character,  outstripped  the  physical 
expositions  lately  in  vogue.  Of  course,  a  virtue  has 
been  made  of  necessity  here. 

We  must  admit,  that  it  is  not  in  our  power  to  de- 
scribe directly  every  fact,  on  the  moment.  Indeed, 
we  should  succumb  in  utter  despair  if  the  whole  wealth 
of  facts  which  we  come  step  by  step  to  know,  were 
presented  to  us  all  at  once.  Happily,  only  detached 
and  unusual  features  first  strike  us.,  and  such  we  bring 
nearer  to  ourselves  by  comparison  with  every-day 
events.  Here  the  notions  of  the  common  speech  are 
first  developed.  The  comparisons  then  grow  more 
manifold  and  numerous,  the  fields  of  facts  compared 


ON  COMPARISON  IN  PHYSICS.  249 

more  extensive,  the  concepts  that  make  direct  descrip- 
tion possible,  proportionately  more  general  and  more 
abstract. 

First  we  become  familiar  with  the  motion  of  freely 
falling  bodies.  The  concepts  of  force,  mass,  and  work 
are  then  carried  over,  with  appropriate  modifications, 
to  the  phenomena  of  electricity  and  magnetism.  A 
stream  of  water  is  said  to  have  suggested  to  Fourier 
the  first  distinct  picture  of  currents  of  heat.  A  special 
case  of  vibrations  of  strings  investigated  by  Taylor, 
cleared  up  for  him  a  special  case  of  the  conduction  of 
heat.  Much  in  the  same  way  that  Daniel  Bernoulli 
and  Euler  constructed  the  most  diverse  forms  of  vi- 
brations of  strings  from  Taylor's  cases,  so  Fourier  con- 
structs out  of  simple  cases  of  conduction  the  most 
multifarious  motions  of  heat;  and  that  method  has 
extended  itself  over  the  whole  of  physics.  Ohm  forms 
his  conception  of  the  electric  current  in  imitation  o( 
Fourier's.  The  latter,  also,  adopts  Fick's  theory  of 
diffusion.  In  an  analogous  manner  a  conception  of 
the  magnetic  current  is  developed.  All  sorts  of  sta- 
tionary currents  are  thus  made  to  exhibit  common 
features,  and  even  the  condition  of  complete  equilib- 
rium in  an  extended  medium  shares  these  features 
with  the  dynamical  condition  of  equilibrium  of  a  sta- 
tionary current.  Things  as  remote  as  the  magnetic 
lines  of  force  of  an  electric  current  and  the  stream- 
lines of  a  frictionless  liquid  vortex  enter  in  this  way 
into  a  peculiar  relationship  of  similarity.  The  con- 


250  ON  COMPARISON  IN  PHYSICS. 

cept  of  potential,  originally  enunciated  for  a  re- 
stricted province,  acquires  a  wide-reaching  applica- 
bility. Things  as  dissimilar  as  pressure,  temperature, 
and  electromotive  force,  now  show  points  of  agree- 
ment in  relation  to  ideas  derived  by  definite  methods 
from  that  concept:  viz.,  fall  of  pressure,  fall  of  tem- 
perature, fall  of  potential,  as  also  with  the  further  no- 
tions of  liquid,  thermal,  and  electric  strength  of  cur- 
rent. That  relationship  between  systems  of  ideas  in 
which  the  dissimilarity  of  every  two  homologous  con- 
cepts as  well  as  the  agreement  in  logical  relations 
of  every  two  homologous  pairs  of  concepts,  is  clearly 
brought  to  light,  is  called  an  analogy.  It  is  an  effective 
means  of  mastering  heterogeneous  fields  of  facts  in 
unitary  comprehension.  The  path  is  plainly  shown  in 
which  a  universal  physical  phenomenology  embracing  all 
domains,  will  be  developed. 

In  the  process  described  we  attain  for  the  first  time 
to  what  is  indispensable  in  the  direct  description  of 
broad  fields  of  fact — the  wide-reaching  abstract  concept. 
And  now  I  must  put  a  question  smacking  of  the  school- 
master, but  unavoidable  :  What  is  a  concept  ?  Is  it  a 
hazy  representation,  admitting  withal  of  mental  visu- 
alisation? No.  Mental  visualisation  accompanies  it 
only  in  the  simplest  cases,  and  then  merely  as  an  ad- 
junct. Think,  for  example,  of  the  "  coefficient  of  self- 
induction,"  and  seek  for  its  visualised  mental  image. 
Or  is,  perhaps,  the  concept  a  mere  word  ?  The  adop- 
tion of  this  forlorn  idea,  which  has  been  actually  pro- 


ON  COMPARISON  IN  PH  YSICS.  25 1 

posed  of  late  by  a  reputed  mathematician  would  only 
throw  us  back  a  thousand  years  into  the  deepest  scho- 
lasticism. We  must,  therefore,  reject  it. 

The  solution  is  not  far  to  seek.  We  must  not  think 
that  sensation,  or  representation,  is  a  purely  passive 
process.  The  lowest  organisms  respond  to  it  with  a 
simple  reflex  motion,  by  engulfing  the  prey  which  ap- 
proaches them.  In  higher  organisms  the  centripetal 
stimulus  encounters  in  the  nervous  system  obstacles 
and  aids  which  modify  the  centrifugal  process.  In  still 
higher  organisms,  where  prey  is  pursued  and  exam- 
ined, the  process  in  question  may  go  through  exten- 
sive paths  of  circular  motions  before  it  comes  to  rel- 
ative rest.  Our  own  life,  too,  is  enacted  in  such 
processes ;  all  that  we  call  science  may  be  regarded 
as  parts,  or  middle  terms,  of  such  activities. 

It  will  not  surprise  us  now  if  I  say :  the  definition 
of  a  concept,  and,  when  it  is  very  familiar,  even  its 
name,  is  an  impulse  to  some  accurately  determined, 
often  complicated,  critical,  comparative,  or  construc- 
tive activity,  the  usually  sense-perceptive  result  of 
which  is  a  term  or  member  of  the  concept's  scope.  It 
matters  not  whether  the  concept  draws  the  attention 
only  to  one  certain  sense  (as  sight)  or  to  a  phase  of  a 
sense  (as  color,  form),  or  is  the  starting-point  of  a 
complicated  action ;  nor  whether  the  activity  in  ques- 
tion (chemical,  anatomical,  and  mathematical  opera- 
tions) is  muscular  or  technical,  or  performed  wholly 
in  the  imagination,  or  only  intimated.  The  concept  is 


252  ON  COMPARISON  IN  PHYSICS, 

to  the  physicist  what  a  musical  note  is  to  a  piano- 
player.  A  trained  physicist  or  mathematician  reads  a 
memoir  like  a  musician  reads  a  score.  But  just  as  the 
piano-player  must  first  learn  to  move  his  fingers  singly 
and  collectively,  before  he  can  follow  his  notes  with- 
out effort,  so  the  physicist  or  mathematician  must  go 
through  a  long  apprenticeship  before  he  gains  con- 
trol, so  to  speak,  of  the  manifold  delicate  innervations 
of  his  muscles  and  imagination.  Think  of  how  fre- 
quently the  beginner  in  physics  or  mathematics  per- 
forms more,  or  less,  than  is  required,  or  of  how  fre- 
quently he  conceives  things  differently  from  what  they 
are !  But  if,  after  having  had  sufficient  discipline,  he 
lights  upon  the  phrase  "coefficient  of  self-induction," 
he  knows  immediately  what  that  term  requires  of  him. 
Long  and  thoroughly  practised  actions,  which  have 
their  origin  in  the  necessity  of  comparing  and  repre- 
senting facts  by  other  facts,  are  thus  the  very  kernel 
of  concepts.  In  fact,  positive  and  philosophical  phi- 
lology both  claim  to  have  established  that  all  roots 
represent  concepts  and  stood  originally  for  muscular 
activities  alone.  The  slow  assent  of  physicists  to 
Kirchhoff's  dictum  now  becomes  intelligible.  They 
best  could  feel  the  vast  amount  of  individual  labor, 
theory,  and  skill  required  before  the  ideal  of  direct 

description  could  be  realised. 

* 
*  * 

Suppose,  now,  the  ideal  of  a  given  province  of 
facts  is  reached.    Does  description  accomplish  all  that 


ON  COMPARISON  IN  PHYSICS.  253 

the  inquirer  can  ask  ?  In  my  opinion,  it  does.  De- 
scription is  a  building  up  of  facts  in  thought,  and  this 
building  up  is,  in  the  experimental  sciences,  often  the 
condition  of  actual  execution.  For  the  physicist,  to 
take  a  special  case,  the  metrical  units  are  the  building- 
stones,  the  concepts  the  directions  for  building,  and 
the  facts  the  result  of  the  building.  Our  mental 
imagery  is  almost  a  complete  substitute  for  the  fact, 
and  by  means  of  it  we  can  ascertain  all  the  fact's  prop- 
erties. We  do  not  know  that  worst  which  we  our- 
selves have  made. 

People  require  of  science  that  it  should  prophesy, 
and  Hertz  uses  that  expression  in  his  posthumous 
Mechanics.  But,  natural  as  it  is,  the  expression  is  too 
narrow.  The  geologist  and  the  palaeontologist,  at  times 
the  astronomer,  and  always  the  historian  and  the  phil- 
ologist, prophesy,  so  to  speak,  backwards.  The  descrip- 
tive sciences,  like  geometry  and  mathematics,  prophesy 
neither  forward  or  backwards,  but  seek  from  given 
conditions  the  conditioned.  Let  us  say  rather :  Sci- 
ence completes  in  thought  facts  that  are  only  partly  given. 
This  is  rendered  possible  by  description,  for  descrip- 
tion presupposes  the  interdependence  of  the  descrip- 
tive elements  :  otherwise  nothing  would  be  described. 

It  is  said,  description  leaves  the  sense  of  causality 
unsatisfied.  In  fact,  many  imagine  they  understand 
motions  better  when  they  picture  to  themselves  the 
pulling  forces;  and  yet  the  accelerations,  the  facts, 
accomplish  more,  without  superfluous  additions.  I 


254  ON  COMPARISON  IN  PHYSICS. 

hope  that  the  science  of  the  future  will  discard  the 
idea  of  cause  and  effect,  as  being  formally  obscure ; 
and  in  my  feeling  that  these  ideas  contain  a  strong 
tincture  of  fetishism,  I  am  certainly  not  alone.  The 
more  proper  course  is,  to  regard  the  abstract  determina- 
tive elements  of  a  fact  as  interdependent,  in  a  purely  logi- 
cal way,  as  the  mathematician  or  geometer  does. 
True,  by  comparison  with  the  will,  forces  are  brought 
nearer  to  our  feeling ;  but  it  may  be  that  ultimately  the 
will  itself  will  be  made  clearer  by  comparison  with  the 
accelerations  of  masses. 

If  we  are  asked,  candidly,  when  is  a  fact  clear  to 
us,  we  must  say  "when  we  can  reproduce  it  by  very 
simple  and  very  familiar  intellectual  operations,  such 
as  the  construction  of  accelerations,  or  the  geometri- 
cal summation  of  accelerations,  and  so  forth."  The 
requirement  of  simplicity  is  of  course  to  the  expert 
a  different  matter  from  what  it  is  to  the  novice.  For 
the  first,  description  by  a  system  of  differential  equa- 
tions is  sufficient ;  for  the  second,  a  gradual  construc- 
tion out  of  elementary  laws  is  required.  The  first 
discerns  at  once  the  connexion  of  the  two  expositions. 
Of  course,  it  is  not  disputed  that  the  artistic  value  of 
materially  equivalent  descriptions  may  not  be  different. 

Most  difficult  is  it  to  persuade  strangers  that  the 
grand  universal  laws  of  physics,  such  as  apply  indis- 
criminately to  material,  electrical,  magnetic,  and  other 
systems,  are  not  essentially  different  from  descriptions. 
As  compared  with  many  sciences,  physics  occupies  in 


ON  COMPARISON  IN  2'HYSICS. 


255 


this  respect  a  position  of  vantage  that  is  easily  ex- 
plained. Take,  for  example,  anatomy.  As  the  anato- 
mist in  his  quest  for  agreements  and  differences  in 
animals  ascends  to  ever  higher  and  higher  classifica- 
tions, the  individual  facts  that  represent  the  ultimate 
terms  of  the  system,  are  still  so  different  that  they 
must  be  singly  noted.  Think,  for  example,  of  the  com- 
mon marks  of  the  Vertebrates,  of  the  class-characters 
of  Mammals  and  Birds  on  the  one  hand  and  of  Fishes 
on  the  other,  of  the  double  circulation  of  the  blood  on 
the  one  hand  and  of  the  single  on  the  other.  In  the 
end,  always  isolated  facts  remain,  which  show  only  a 
slight  likeness  to  one  another. 

A  science  still  more  closely  allied  to  physics,  chem- 
istry, is  often  in  the  same  strait.  The  abrupt  change 
of  the  qualitative  properties,  in  all  likelihood  condi- 
tioned by  the  slight  stability  of  the  intermediate  states, 
the  remote  resemblance  of  the  co-ordinated  facts  of 
chemistry  render  the  treatment  of  its  data  difficult. 
Pairs  of  bodies  of  different  qualitative  properties  unite 
in  different  mass-ratios ;  but  no  connexion  between 
the  first  and  the  last  is  to  be  noted,  at  first. 

Physics,  on  the  other  hand,  reveals  to  us  wide  do- 
mains of  qualitatively  homogeneous  facts,  differing  from 
one  another  only  in  the  number  of  equal  parts  into 
which  their  characteristic  marks  are  divisible,  that  is, 
differing  only  quantitatively.  Even  where  we  have  to 
deal  with  qualities  (colors  and  sounds),  quantitative 
characters  of  those  qualities  are  at  our  disposal.  Here 


256  ON  COMPARISON  IN  PHYSICS. 

the  classification  is  so  simple  a  task  that  it  rarely  im- 
presses us  as  such,  whilst  in  infinitely  fine  gradations, 
in  a  continuum  of  facts,  our  number-system  is  ready  be- 
forehand to  follow  as  far  as  we  wish.  The  co-ordinated 
facts  are  here  extremely  similar  and  very  closely  af- 
fined, as  are  also  their  descriptions  which  consist  in 
the  determination  of  the  numerical  measures  of  one 
given  set  of  characters  from  those  of  a  different  set  by 
means  of  familiar  mathematical  operations — methods 
of  derivation.  Thus,  the  common  characteristics  of 
all  descriptions  can  be  found  here  ;  and  with  them  a 
succinct,  comprehensive  description,  or  a  rule  for  the 
construction  of  all  single  descriptions,  is  assigned, — 
and  this  we  call  law.  Well-known  examples  are  the 
formulae  for  freely  falling  bodies,  for  projectiles,  for 
central  motion,  and  so  forth.  If  physics  apparently 
accomplishes  more  by  its  methods  than  other  sciences, 
we  must  remember  that  in  a  sense  it  has  presented  to 
it  much  simpler  problems. 

The  remaining  sciences,  whose  facts  also  present  a 
physical  side,  need  not  be  envious  of  physics  for  this 
superiority  ;  for  all  its  acquisitions  ultimately  redound 
to  their  benefit  as  well.  But  also  in  other  ways  this 
mutual  help  shall  and  must  change.  Chemistry  has  ad- 
vanced very  far  in  making  the  methods  of  physics  her 
own.  Apart  from  older  attempts,  the  periodical  series 
of  Lothar  Meyer  and  Mendelejeff  are  a  brilliant  and 
adequate  means  of  producing  an  easily  surveyed  sys- 
tem of  facts,  which  by  gradually  becoming  complete, 


ON  COMPARISON  IN  PHYSICS,  257 

will  take  the  place  almost  of  a  continuum  of  facts. 
Further,  by  the  study  of  solutions,  of  dissociation,  in 
fact  generally  of  phenomena  which  present  a  contin- 
uum of  cases,  the  methods  of  thermodynamics  have 
found  entrance  into  chemistry.  Similarly  we  may  hope 
that,  at  some  future  day,  a  mathematician,  letting  the 
fact-continuum  of  embryology  play  before  his  mind, 
which  the  palaeontologists  of  the  future  will  supposedly 
have  enriched  with  more  intermediate  and  derivative 
forms  between  Saurian  and  Bird  than  the  isolated 
Pterodactyl,  Archaeopteryx,  Ichthyornis,  and  so  forth, 
which  we  now  have — that  such  a  mathematician  shall 
transform,  by  the  variation  of  a  few  parameters,  as  in 
a  dissolving  view,  one  form  into  another,  just  as  we 
transform  one  conic  section  into  another. 

Reverting  now  to  Kirchhoff's  words,  we  can  come 
to  some  agreement  regarding  their  import.  Nothing 
can  be  built  without  building-stones,  mortar,  scaffold- 
ing, and  a  builder's  skill.  Yet  assuredly  the  wish  is 
well  founded,  that  will  show  to  posterity  the  complete 
structure  in  its  finished  form,  bereft  of  unsightly  scaf- 
folding. It  is  the  pure  logical  and  aesthetic  sense  of  the 
mathematician  that  speaks  out  of  Kirchhoff's  words. 
Modern  expositions  of  physics  aspire  after  his  ideal ; 
that,  too,  is  intelligible.  But  it  would  be  a  poor  di- 
dactic shift,  for  one  whose  business  it  was  to  train 
architects,  to  say:  "Here  is  a  splendid  edifice;  if  thou 
wouldst  really  build,  go  thou  and  do  likewise. 

The  barriers  between  the  special  sciences,  which 


258  ON  COMPARISON  IN  PHYSICS. 

make  division  of  work  and  concentration  possible,  but 
which  appear  to  us  after  all  as  cold  and  conventional 
restrictions,  will  gradually  disappear.  Bridge  upon 
bridge  is  thrown  over  the  gaps.  Contents  and  meth- 
ods, even  of  the  remotest  branches,  are  compared. 
When  the  Congress  of  Natural  Scientists  shall  meet  a 
hundred  years  hence,  we  may  expect  that  they  will 
represent  a  unity  in  a  higher  sense  than  is  possible  to- 
day, not  in  sentiment  and  aim  alone,  but  in  method 
also.  In  the  meantime,  this  great  change  will  be 
helped  by  our  keeping  constantly  before  our  minds  the 
fact  of  the  intrinsic  relationship  of  all  research,  which 
Kirchhoff  characterised  with  such  classical  simplicity. 


THE  PART  PLAYED  BY  ACCIDENT  IN 
INVENTION  AND  DISCOVERY.* 


TT  IS  CHARACTERISTIC  of  the  naive  and  san- 
^  guine  beginnings  of  thought  in  youthful  men  and 
nations,  that  all  problems  are  held  to  be  soluble  and 
fundamentally  intelligible  on  the  first  appearance  of 
success.  The  sage  of  Miletus,  on  seeing  plants  take 
their  rise  from  moisture,  believed  he  had  compre- 
hended the  whole  of  nature,  and  he  of  Samos,  on  dis- 
covering that  definite  numbers  corresponded  to  the 
lengths  of  harmonic  strings,  imagined  he  could  ex- 
haust the  nature  of  the  world  by  means  of  numbers. 
Philosophy  and  science  in  such  periods  are  blended. 
Wider  experience,  however,  speedily  discloses  the 
error  of  such  a  course,  gives  rise  to  criticism,  and 
leads  to  the  division  and  ramification  of  the  sciences. 
At  the  same  time,  the  necessity  of  a  broad  and 
general  view  of  the  world  remains  ;  and  to  meet  this 
need  philosophy  parts  company  with  special  inquiry. 

'Inaugural  lecture  delivered  on  assuming  the  Professorship  of  the  His- 
tory and  Theory  of  Inductive  Science  in  the  University  of  Vienna,  October 

21,  1895. 


260    ACCIDENT  IN  INVENTION  AND  DISCOVERY. 

It  is  true,  the  two  are  often  found  united  in  gigantic 
personalities.  But  as  a  rule  their  ways  diverge  more 
and  more  widely  from  each  other.  And  if  the  estrange- 
ment of  philosophy  from  science  can  reach  a  point 
where  data  unworthy  of  the  nursery  are  not  deemed  too 
scanty  as  foundations  of  the  world,  on  the  other  hand 
the  thorough-paced  specialist  may  go  to  the  extreme 
of  rejecting  point-blank  the  possibility  of  a  broader 
view,  or  at  least  of  deeming  it  superfluous,  forgetful 
of  Voltaire's  apophthegm,  nowhere  more  applicable 
than  here,  Le  superflu — chose  tres  ntcessaire. 

It  is  true,  the  history  of  philosophy,  owing  to  the 
insufficiency  of  its  constructive  data,  is  and  must  be 
largely  a  history  of  error.  But  it  would  be  the  height 
of  ingratitude  on  our  part  to  forget  that  the  seeds  of 
thoughts  which  still  fructify  the  soil  of  special  re- 
search, such  as  the  theory  of  irrationals,  the  concep- 
tions of  conservation,  the  doctrine  of  evolution,  the 
idea  of  specific  energies,  and  so  forth,  may  be  traced 
back  in  distant  ages  to  philosophical  sources.  Fur- 
thermore, to  have  deferred  or  abandoned  the  attempt 
at  a  broad  philosophical  view  of  the  world  from  a  full 
knowledge  of  the  insufficiency  of  our  materials,  is 
quite  a  different  thing  from  never  having  undertaken 
it  at  all.  The  revenge  of  its  neglect,  moreover,  is 
constantly  visited  upon  the  specialist  by  his  commit- 
tal of  the  very  errors  which  philosophy  long  ago  ex- 
posed. As  a  fact,  in  physics  and  physiology,  par- 
ticularly during  the  first  half  of  this  century,  are  to  be 


ACCIDENT  IN  INVENTION  AND  DISCOVERY.    261 

met  intellectual  productions  which  for  naive  simplicity 
are  not  a  jot  inferior  to  those  of  the  Ionian  school,  or 
to  the  Platonic  ideas,  or  to  that  much  reviled  onto- 
togical  proof. 

Latterly,  there  has  been  evidence  of  a  gradual 
change  in  the  situation.  Recent  philosophy  has  set 
itself  more  modest  and  more  attainable  ends;  it  is 
no  longer  inimical  to  special  inquiry;  in  fact,  it  is 
zealously  taking  part  in  that  inquiry.  On  the  other 
hand,  the  special  sciences,  mathematics  and  physics, 
no  less  than  philology,  have  become  eminently  phil- 
osophical. The  material  presented  is  no  longer  ac- 
cepted uncritically.  The  glance  of  the  inquirer  is 
bent  upon  neighboring  fields,  whence  that  material 
has  been  derived.  The  different  special  departments 
are  striving  for  closer  union,  and  gradually  the  con- 
viction is  gaining  ground  that  philosophy  can  consist 
only  of  mutual,  complemental  criticism,  interpenetra- 
tion,  and  union  of  the  special  sciences  into  a  consoli- 
dated whole.  As  the  blood  in  nourishing  the  body 
separates  into  countless  capillaries,  only  to  be  col- 
lected again  and  to  meet  in  the  heart,  so  in  the  science 
of  the  future  all  the  rills  of  knowledge  will  gather 
more  and  more  into  a  common  and  undivided  stream. 

It  is  this  view — not  an  unfamiliar  one  to  the  pres- 
ent generation— that  I  purpose  to  advocate.  Enter- 
tain no  hope,  or  rather  fear,  that  I  shall  construct 
systems  for  you.  I  shall  remain  a  natural  inquirer. 
Nor  expect  that  it  is  my  intention  to  skirt  all  the 


262    ACCIDENT  IN  INVENTION  AND  DISCOVERY. 

fields  of  natural  inquiry.  I  can  attempt  to  be  your 
guide  only  in  that  branch  which  is  familiar  to  me,  and 
even  there  I  can  assist  in  the  furtherment  of  only  a 
small  portion  of  the  allotted  task.  If  I  shall  succeed 
in  rendering  plain  to  you  the  relations  of  physics, 
psychology,  and  the  theory  of  knowledge,  so  that  you 
may  draw  from  each  profit  and  light,  redounding  to 
the  advantage  of  each,  I  shall  regard  my  work  as  not 
having  been  in  vain.  Therefore,  to  illustrate  by  an 
example  how,  consonantly  with  my  powers  and  views, 
I  conceive  such  inquiries  should  be  conducted,  I  shall 
treat  to-day,  in  the  form  of  a  brief  sketch,  of  the  fol- 
lowing special  and  limited  subject — of  the  part  which 
accidental  circumstances  play  in  the  development  of  inven- 
tions and  discoveries. 

* 
*  * 

When  we  Germans  say  of  a  man  that  he  was  not 
the  inventor  of  gunpowder,*  we  impliedly  cast  a  grave 
suspicion  on  his  abilities.  But  the  expression  is  not 
a  felicitous  one,  as  there  is  probably  no  invention  in 
which  deliberate  thought  had  a  smaller,  and  pure  luck 
a  larger,  share  than  in  this.  It  is  well  to  ask,  Are  we 
justified  in  placing  a  low  estimate  on  the  achievement 
of  an  inventor  because  accident  has  assisted  him  in 
his  work?  Huygens,  whose  discoveries  and  inven- 
tions are  justly  sufficient  to  entitle  him  to  an  opinion 
in  such  matters,  lays  great  emphasis  on  this  factor. 
He  asserts  that  a  man  capable  of  inventing  the  tele- 

*  The  phrase  is,  Er  hat  das  Pulver  nickt  erfunden. 


ACCIDENT  IN  INVENTION  AND  DISCOVERY.    263 

scope  without  the  concurrence  of  accident  must  have 
been  gifted  with  superhuman  genius.* 

A  man  living  in  the  midst  of  civilisation  finds  him- 
self surrounded  by  a  host  of  marvellous  inventions, 
considering  none  other  than  the  means  of  satisfying 
the  needs  of  daily  life.  Picture  such  a  man  trans- 
ported to  the  epoch  preceding  the  invention  of  these 
ingenious  appliances,  and  imagine  him  undertaking 
in  a  serious  manner  to  comprehend  their  origin.  At 
first  the  intellectual  power  of  the  men  capable  of  pro- 
ducing such  marvels  will  strike  him  as  incredible,  or, 
if  we  adopt  the  ancient  view,  as  divine.  But  his  as- 
tonishment is  considerably  allayed  by  the  disenchant- 
ing yet  elucidative  revelations  of  the  history  of  primi- 
tive culture,  which  to  a  large  extent  prove  that  these 
inventions  took  their  rise  very  slowly  and  by  imper- 
ceptible degrees. 

A  small  hole  in  the  ground  with  fire  kindled  in  it 
constituted  the  primitive  stove.  The  flesh  of  the 
quarry,  wrapped  with  water  in  its  skin,  was  boiled  by 
contact  with  heated  stones.  Cooking  by  stones  was 
also  done  in  wooden  vessels.  Hollow  gourds  were 
protected  from  the  fire  by  coats  of  clay.  Thus,  from 
the  burned  clay  accidentally  originated  the  enveloping 
pot,  which  rendered  the  gourd  superfluous,  although 


*  Quod  si  quis  tanta  industria  exstitisset,  ut  ex  naturae  principiit  et  geo- 
metria  hanc  rem  eruere  potuisset,  eum  ego  supra  mortaliuin  sortcni  ingenio 
valuisse  dicenduin  crederem.  Sed  hoc  tantuin  abest,  ut  fortuito  reperti  arti- 
ficii  rationem  non  adhuc  satis  explicari  potuerint  viri  doctissimi."— Hugenii 
Dioptrica  (de  telescopiis). 


264    ACCIDENT  IN  INVENTION  AND  DISCOVERY. 

for  a  long  time  thereafter  the  clay  was  still  spread 
over  the  gourd,  or  pressed  into  woven  wicker-work 
before  the  potter's  art  assumed  its  final  independence. 
Even  then  the  wicker-work  ornament  was  retained,  as 
a  sort  of  attest  of  its  origin. 

We  see,  thus,  it  is  by  accidental  circumstances,  or 
by  such  as  lie  without  our  purpose,  foresight,  and 
power,  that  man  is  gradually  led  to  the  acquaintance 
of  improved  means  of  satisfying  his  wants.  Let  the 
reader  picture  to  himself  the  genius  of  a  man  who 
could  have  foreseen  without  the  help  of  accident  that 
clay  handled  in  the  ordinary  manner  would  produce  a 
useful  cooking  utensil !  The  majority  of  the  inven- 
tions made  in  the  early  stages  of  civilisation,  includ- 
ing language,  writing,  money,  and  the  rest,  could  not 
have  been  the  product  of  deliberate  methodical  re- 
flexion for  the  simple  reason  that  no  idea  of  their 
value  and  significance  could  have  been  had  except 
from  practical  use.  The  invention  of  the  bridge  may 
have  been  suggested  by  the  trunk  of  a  tree  which  had 
fallen  athwart  a  mountain-torrent ;  that  of  the  tool  by 
the  use  of  a  stone  accidentally  taken  into  the  hand  to 
crack  nuts.  The  use  of  fire  probably  started  in  and 
was  disseminated  from  regions  where  volcanic  erup- 
tions, hot  springs,  and  burning  jets  of  natural  gas 
afforded  opportunity  for  quietly  observing  and  turn- 
ing to  practical  account  the  properties  of  fire.  Only 
after  that  had  been  done  could  the  significance  of  the 
fire-drill  be  appreciated,  an  instrument  which  was 


ACCIDENT  IN  INVENTION  AND  DISCOVERY.    265 

probably  discovered  from  boring  a  hole  through  a 
piece  of  wood.  The  suggestion  of  a  distinguished  in- 
quirer that  the  invention  of  the  fire-drill  originated  on 
the  occasion  of  a  religious  ceremony  is  both  fantastic 
and  incredible.  And  as  to  the  use  of  fire,  we  should 
no  more  attempt  to  derive  that  from  the  invention  of 
the  fire-drill  than  we  should  from  the  invention  of  sul- 
phur matches.  Unquestionably  the  opposite  course 
was  the  real  one.* 

Similar  phenomena,  though  still  largely  veiled  in 
obscurity,  mark  the  initial  transition  of  nations  from 
a  hunting  to  a  nomadic  life  and  to  agriculture.!  We 
shall  not  multiply  examples,  but  content  ourselves 
with  the  remark  that  the  same  phenomena  recur  in 
historical  times,  in  the  ages  of  great  technical  inven- 
tions, and,  further,  that  regarding  them  the  most 
whimsical  notions  have  been  circulated — notions  which 
ascribe  to  accident  an  unduly  exaggerated  part,  and 
one  which  in  a  psychological  respect  is  absolutely  im- 
possible. The  observation  of  steam  escaping  from  a 
tea-kettle  and  of  the  clattering  of  the  lid  is  supposed 
to  have  led  to  the  invention  of  the  steam-engine.  Just 
think  of  the  gap  between  this  spectacle  and  the  con- 
ception of  the  performance  of  great  mechanical  work 
by  steam,  for  a  man  totally  ignorant  of  the  steam- 
engine  !  Let  us  suppose,  however,  that  an  engineer, 

*I  must  not  be  understood  as  saying  that  the  fire-drill  has  played  no  parl 
in  the  worship  of  fire  or  of  the  sun. 

t  Compare  on  this  point  the  extremely  interesting  remarks  of  Dr  Paul 
Carus  in  his  Philosophy  of  the  Tool,  Chicago,  1893. 


266    ACCIDENT  IN  INVENTION  AND  DISCOVERY. 

versed  in  the  practical  construction  of  pumps,  should 
accidentally  dip  into  water  an  inverted  bottle  that  had 
been  filled  with  steam  for  drying  and  still  retained  its 
steam.  He  would  see  the  water  rush  violently  into 
the  bottle,  and  the  idea  would  very  naturally  suggest 
itself  of  founding  on  this  experience  a  convenient  and 
useful  atmospheric  steam-pump,  which  by  impercept- 
ible degrees,  both  psychologically  possible  and  imme- 
diate, would  then  undergo  a  natural  and  gradual  trans- 
formation into  Watt's  steam-engine. 

But  granting  that  the  most  important  inventions 
are  brought  to  man's  notice  accidentally  and  in  ways 
that  are  beyond  his  foresight,  yet  it  does  not  follow 
that  accident  alone  is  sufficient  to  produce  an  inven- 
tion. The  part  which  man  plays  is  by  no  means  a 
passive  one.  Even  the  first  potter  in  the  primeval 
forest  must  have  felt  some  stirrings  of  genius  within 
him.  In  all  such  cases,  the  inventor  is  obliged  to  take 
note  of  the  new  fact,  he  must  discover  and  grasp  its 
advantageous  feature,  and  must  have  the  power  to 
turn  that  feature  to  account  in  the  realisation  of  his 
purpose.  He  must  isolate  the  new  feature,  impress  it 
upon  his  memory,  unite  and  interweave  it  with  the 
rest  of  his  thought ;  in  short,  he  must  possess  the  ca- 
pacity to  profit  by  experience, 

The  capacity  to  profit  by  experience  might  well  be 
set  up  as  a  test  of  intelligence.  This  power  varies 
considerably  in  men  of  the  same  race,  and  increases 
enormously  as  we  advance  from  the  lower  animals  to 


ACCIDENT  IN  INVENTION  AND  DISCOVERY.    267 

man.  The  former  are  limited  in  this  regard  almost 
entirely  to  the  reflex  actions  which  they  have  inherited 
with  their  organism,  they  are  almost  totally  incapable 
of  individual  experience,  and  considering  their  simple 
wants  are  scarcely  in  need  of  it.  The  ivory-snail 
(Eburna  spirata)  never  learns  to  avoid  the  carnivorous 
Actinia,  no  matter  how  often  it  may  wince  under  the 
latter's  shower  of  needles,  apparently  having  no  mem- 
ory for  pain  whatever.*  A  spider  can  be  lured  forth 
repeatedly  from  its  hole  by  touching  its  web  with  a 
tuning-fork.  The  moth  plunges  again  and  again  into 
the  flame  which  has  burnt  it.  The  humming-bird 
hawk-moth  f  dashes  repeatedly  against  the  painted 
roses  of  the  wall-paper,  like  the  unhappy  and  desper- 
ate thinker  who  never  wearies  of  attacking  the  same 
insoluble  chimerical  problem.  As  aimlessly  almost  as 
Maxwell's  gaseous  molecules  and  in  the  same  unrea- 
soning manner  common  flies  in  their  search  for  light 
and  air  stream  against  the  glass  pane  of  a  half-opened 
window  and  remain  there  from  sheer  inability  to  find 
their  way  around  the  narrow  frame.  But  a  pike  sep- 
arated from  the  minnows  of  his  aquarium  by  a  glass 
partition,  learns  after  the  lapse  of  a  few  months, 
though  only  after  having  butted  himself  half  to  death, 
that  he  cannot  attack  these  fishes  with  impunity. 
What  is  more,  he  leaves  them  in  peace  even  after  the 

*Mobius,  Natunvissenschaftlichtr  Vtrti*  fllr  ScUtnrig-Holstrin,  Kiel, 
1893,  p.  113  et  seq. 

tl  am  indebted  for  this  observation  to  Professor  Hattcheck. 


268    ACCIDENT  IN  INVENTION  AND  DISCOVERY. 

removal  of  the  partition,  though  he  will  bolt  a  strange 
fish  at  once.  Considerable  memory  must  be  attrib- 
uted to  birds  of  passage,  a  memory  which,  probably 
owing  to  the  absence  of  disturbing  thoughts,  acts  with 
the  precision  of  that  of  some  idiots.  Finally,  the 
susceptibility  to  training  evinced  by  the  higher  verte- 
brates is  indisputable  proof  of  the  ability  of  these  ani- 
mals to  profit  by  experience. 

A  powerfully  developed  mechanical  memory,  which 
recalls  vividly  and  faithfully  old  situations,  is  sufficient 
for  avoiding  definite  particular  dangers,  or  for  taking 
advantage  of  definite  particular  opportunities.  But 
more  is  required  for  the  development  of  inventions. 
More  extensive  chains  of  images  are  necessary  here, 
the  excitation  by  mutual  contact  of  widely  different 
trains  of  ideas,  a  more  powerful,  more  manifold,  and 
richer  connexion  of  the  contents  of  memory,  a  more 
powerful  and  impressionable  psychical  life,  heightened 
by  use.  A  man  stands  on  the  bank  of  a  mountain- 
torrent,  which  is  a  serious  obstacle  to  him.  He  re- 
members that  he  has  crossed  just  such  a  torrent  be- 
fore on  the  trunk  of  a  fallen  tree.  Hard  by  trees  are 
growing.  He  has  often  moved  the  trunks  of  fallen 
trees.  He  has  also  felled  trees  before,  and  then  moved 
them.  To  fell  trees  he  has  used  sharp  stones.  He 
goes  in  search  of  such  a  stone,  and  as  the  old  situations 
that  crowd  into  his  memory  and  are  held  there  in  liv- 
ing reality  by  the  definite  powerful  interest  which  he 
has  in  crossing  just  this  torrent,— as  these  impressions 


ACCIDENT  IN  INVENTION  AND  DISCOVERY.    269 

are  made  to  pass  before  his  mind  in  the  inverse  order  in 
which  they  were  here  evoked,  he  invents  the  bridge. 

There  can  be  no  doubt  but  the  higher  vertebrates 
adapt  their  actions  in  some  moderate  degree  to  cir- 
cumstances. The  fact  that  they  give  no  appreciable 
evidence  of  advance  by  the  accumulation  of  inven- 
tions, is  satisfactorily  explained  by  a  difference  of  de- 
gree or  intensity  of  intelligence  as  compared  with 
man;  the  assumption  of  a  difference  of  kind  is  not 
necessary.  A  person  who  saves  a  little  every  day,  be 
it  ever  so  little,  has  an  incalculable  advantage  over 
him  who  daily  squanders  that  amount,  or  is  unable  to 
keep  what  he  has  accumulated.  A  slight  quantitative 
difference  in  such  things  explains  enormous  differ- 
ences of  advancement. 

The  rules  which  hold  good  in  prehistoric  times 
also  hold  good  in  historical  times,  and  the  remarks 
made  on  invention  may  be  applied  almost  without 
modification  to  discovery;  for  the  two  are  distin- 
guished solely  by  the  use  to  which  the  new  knowledge 
is  put.  In  both  cases  the  investigator  is  concerned 
with  some  newly  observed  relation  of  new  or  old  prop- 
erties, abstract  or  concrete.  It  is  observed,  for  exam- 
ple, that  a  substance  which  gives  a  chemical  reaction 
A  is  also  the  cause  of  a  chemical  reaction  B.  If  this 
observation  fulfils  no  purpose  but  that  of  furthering 
the  scientist's  insight,  or  of  removing  a  source  of  in- 
tellectual discomfort,  we  have  a  discovery;  but  an  in- 
vention, if  in  using  the  substance  giving  the  reaction 


270    ACCIDENT  IN  INVENTION  AND  DISCOVERY. 

A  to  produce  the  desired  reaction  B,  we  have  a  prac- 
tical end  in  view,  and  seek  to  remove  a  source  of  ma- 
terial discomfort.  The  phrase,  disclosure  of  the  connex- 
ion of  reactions,  is  broad  enough  to  cover  discoveries 
and  inventions  in  all  departments.  It  embraces  the 
Pythagorean  proposition,  which  is  a  combination  of  a 
geometrical  and  an  arithmetical  reaction,  Newton's 
discovery  of  the  connexion  of  Kepler's  motions  with 
the  law  of  the  inverse  squares,  as  perfectly  as  it  does 
the  detection  of  some  minute  but  appropriate  altera- 
tion in  the  construction  of  a  tool,  or  of  some  appro- 
priate change  in  the  methods  of  a  dyeing  establish- 
ment. 

The  disclosure  of  new  provinces  of  facts  before 
unknown  can  only  be  brought  about  by  accidental  cir- 
cumstances, under  which  are  remarked  facts  that  com- 
monly go  unnoticed.  The  achievement  of  the  discov- 
erer here  consists  in  his  sharpened  attention,  which 
detects  the  uncommon  features  of  an  occurrence  and 
their  determining  conditions  from  their  most  evanes- 
cent marks,*  and  discovers  means  of  submitting  them 
to  exact  and  full  observation.  Under  this  head  be- 
long the  first  disclosures  of  electrical  and  magnetic 
phenomena,  Grimaldi's  observation  of  interference, 
Arago's  discovery  of  the  increased  check  suffered  by  a 
magnetic  needle  vibrating  in  a  copper  envelope  as 
compared  with  that  observed  in  a  bandbox,  Foucault's 
observation  of  the  stability  of  the  plane  of  vibration 

*  Cf.  Hoppe,  Entdecken  und  Findtn.    1870. 


ACCIDENT  IN  INVENTION  AND  DISCOVERY.    271 

of  a  rod  accidentally  struck  while  rotating  in  a  turn- 
ing-lathe, Mayer's  observation  of  the  increased  red- 
ness of  venous  blood  in  the  tropics,  Kirchhoff's  obser- 
vation of  the  augmentation  of  the  ZMine  in  the  solar 
spectrum  by  the  interposition  of  a  sodium  lamp, 
Schonbein's  discovery  of  ozone  from  the  phosphoric 
smell  emitted  on  the  disruption  of  air  by  electric 
sparks,  and  a  host  of  others.  All  these  facts,  of  which 
unquestionably  many  were  seen  numbers  of  times  be- 
fore they  were  noticed,  are  examples  of  the  inaugura- 
tion of  momentous  discoveries  by  accidental  circum- 
stances, and  place  the  importance  of  strained  attention 
in  a  brilliant  light. 

But  not  only  is  a  significant  part  played  in  the  be- 
ginning of  an  inquiry  by  co-operative  circumstances 
beyond  the  foresight  of  the  investigator;  their  influence 
is  also  active  in  its  prosecution.  Dufay,  thus,  whilst 
following  up  the  behavior  of  one  electrical  state  which 
he  had  assumed,  discovers  the  existence  of  two.  Fres- 
nel  learns  by  accident  that  the  interference-bands  re- 
ceived on  ground  glass  are  seen  to  better  advantage 
in  the  open  air.  The  diffraction-phenomenon  of  two 
slits  proved  to  be  considerably  different  from  what 
Fraunhofer  had  anticipated,  and  in  following  up  this 
circumstance  he  was  led  to  the  important  discovery  of 
grating-spectra.  Faraday's  induction-phenomenon  de- 
parted widely  from  the  initial  conception  which  occa- 
sioned his  experiments,  and  it  is  precisely  this  devia- 
tion that  constitutes  his  real  discovery. 


272    ACCIDENT  IN  INVENTION  AND  DISCOVERY. 

Every  man  has  pondered  on  some  subject.  Every 
one  of  us  can  multiply  the  examples  cited,  by  less  il- 
lustrious ones  from  his  own  experience.  I  shall  cite 
but  one.  On  rounding  a  railway  curve  once,  I  acci- 
dentally remarked  a  striking  apparent  inclination  of 
the  houses  and  trees.  I  inferred  that  the  direction  of 
the  total  resultant  physical  acceleration  of  the  body 
reacts  physiologically  as  the  vertical.  Afterwards,  in 
attempting  to  inquire  more  carefully  into  this  phe- 
nomenon, and  this  only,  in  a  large  whirling  machine, 
the  collateral  phenomena  conducted  me  to  the  sensa- 
tion of  angular  acceleration,  vertigo,  Flouren's  ex- 
periments on  the  section  of  the  semi-circular  canals 
etc.,  from  which  gradually  resulted  views  relating  to 
sensations  of  direction  which  are  also  held  by  Breuer 
and  Brown,  which  were  at  first  contested  on  all  hands, 
but  are  now  regarded  on  many  sides  as  correct,  and 
which  have  been  recently  enriched  by  the  interesting 
inquiries  of  Breuer  concerning  the  macula  acustica,  and 
Kreidel's  experiments  with  magnetically  orientable 
Crustacea.*  Not  disregard  of  accident  but  a  direct  and 
purposeful  employment  of  it  advances  research. 

The  more  powerful  the  psychical  connexion  of  the 
memory  pictures  is, — and  it  varies  with  the  individual 
and  the  mood, — the  more  apt  is  the  same  accidental 
observation  to  be  productive  of  results.  Galileo  knows 
that  the  air  has  weight;  he  also  knows  of  the  "re- 
sistance to  a  vacuum,"  expressed  both  in  weight  and 

*  See  the  lecture  "  Sensations  of  Orientation,"  p.  282  et  seq. 


ACCIDENT  IN  INVENTION  AND  DISCOVERY.    273 

in  the  height  of  a  column  of  water.  But  the  two  ideas 
dwelt  asunder  in  his  mind.  It  remained  for  Torricelli 
to  vary  the  specific  gravity  of  the  liquid  measuring  the 
pressure,  and  not  till  then  was  the  air  included  in  the 
list  of  pressure-exerting  fluids.  The  reversal  of  the 
lines  of  the  spectrum  was  seen  repeatedly  before 
Kirchhoff,  and  had  been  mechanically  explained.  But 
it  was  left  for  his  penetrating  vision  to  discern  the 
evidence  of  the  connexion  of  this  phenomenon  with 
questions  of  heat,  and  to  him  alone  through  persistent 
labor  was  revealed  the  sweeping  significance  of  the 
fact  for  the  mobile  equilibrium  of  heat.  Supposing, 
then,  that  such  a  rich  organic  connexion  of  the  ele- 
ments of  memory  exists,  and  is  the  prime  distinguish- 
ing mark  of  the  inquirer,  next  in  importance  certainly 
is  that  intense  interest  in  a  definite  object,  in  a  definite 
idea,  which  fashions  advantageous  combinations  of 
thought  from  elements  before  disconnected,  and  ob- 
trudes that  idea  into  every  observation  made,  and  into 
every  thought  formed,  making  it  enter  into  relation- 
ship with  all  things.  Thus  Bradley,  deeply  engrossed 
with  the  subject  of  aberration,  is  led  to  its  solution 
by  an  exceedingly  unobtrusive  experience  in  crossing 
the  Thames.  It  is  permissible,  therefore,  to  ask 
whether  accident  leads  the  discoverer,  or  the  discov- 
erer accident,  to  a  successful  outcome  in  scientific 
quests. 

No  man  should  dream  of  solving  a  great  problem 
unless  he  is  so  thoroughly  saturated  with  his  subject 


274    ACCIDENT  IN  INVENTION  AND  DISCOVERY. 

that  everything  else  sinks  into  comparative  insignifi- 
cance. During  a  hurried  meeting  with  Mayer  in  Hei- 
delberg once,  Jolly  remarked,  with  a  rather  dubious 
implication,  that  if  Mayer's  theory  were  correct  water 
could  be  warmed  by  shaking.  Mayer  went  away  with- 
out a  word  of  reply.  Several  weeks  later,  and  now 
unrecognised  by  Jolly,  he  rushed  into  the  latter's  pres- 
ence exclaiming:  "Es  ischt  aso!"  (It  is  so,  it  is 
so  !)  It  was  only  after  considerable  explanation  that 
Jolly  found  out  what  Mayer  wanted  to  say.  The  inci- 
dent needs  no  comment* 

A  person  deadened  to  sensory  impressions  and 
given  up  solely  to  the  pursuit  of  his  own  thoughts, 
may  also  light  on  an  idea  that  will  divert  his  mental 
activity  into  totally  new  channels.  In  such  cases  it  is 
a  psychical  accident,  an  intellectual  experience,  as 
distinguished  from  a  physical  accident,  to  which  the 
person  owes  his  discovery — a  discovery  which  is  here 
made  "deductively"  by  means  of  mental  copies  of  the 
world,  instead  of  experimentally.  Purely  experimental 
inquiry,  moreover,  does  not  exist,  for,  as  Gauss  says, 
virtually  we  always  experiment  with  our  thoughts. 
And  it  is  precisely  that  constant,  corrective  inter- 
change or  intimate  union  of  experiment  and  deduc- 
tion, as  it  was  cultivated  by  Galileo  in  his  Dialogues 
and  by  Newton  in  his  Optics,  that  is  the  foundation  of 
the  benign  fruitfulness  of  modern  scientific  inquiry  as 

*This  story  was  related  to  me  by  Jolly,  and  subsequently  repeated  la  a 
letter  from  him. 


ACCIDENT  IN  INVENTION  AND  DISCOVERY.    275 

contrasted  with  that  of  antiquity,  where  observation 
and  reflexion  ofttimes  pursued  their  respective  courses 
like  two  strangers. 

We  have  to  wait  for  the  appearance  of  a  favorable 
physical  accident.  The  movement  of  our  thoughts 
obeys  the  law  of  association.  In  the  case  of  meagre 
experience  the  result  of  this  law  is  simply  the  mechan- 
ical reproduction  of  definite  sensory  experiences.  On 
the  other  hand,  if  the  psychical  life  is  subjected  to  the 
incessant  influences  of  a  powerful  and  rich  experience, 
then  every  representative  element  in  the  mind  is  con- 
nected with  so  many  others  that  the  actual  and  natural 
course  of  the  thoughts  is  easily  influenced  and  deter- 
mined by  insignificant  circumstances,  which  accident- 
ally are  decisive.  Hereupon,  the  process  termed  ima- 
gination produces  its  protean  and  infinitely  diversified 
forms.  Now  what  can  we  do  to  guide  this  process, 
seeing  that  the  combinatory  law  of  the  images  is  with- 
out our  reach  ?  Rather  let  us  ask,  what  influence  can 
a  powerful  and  constantly  recurring  idea  exert  on  the 
movement  of  our  thoughts?  According  to  what  has 
preceded,  the  answer  is  involved  in  the  question  itself. 
The  idea  dominates  the  thought  of  the  inquirer,  not 
the  latter  the  former. 

Let  us  see,  now,  if  we  can  acquire  a  profounder 
insight  into  the  process  of  discovery.  The  condition 
of  the  discoverer  is,  as  James  has  aptly  remarked,  not 
unlike  the  situation  of  a  person  who  is  trying  to  re- 
member something  that  he  has  forgotten.  Both  are 


276    ACCIDENT  IN  INVENTION  AND  DISCOVERY. 

sensible  of  a  gap,  and  have  only  a  remote  presenti- 
ment of  what  is  missing.  Suppose  I  meet  in  a  com- 
pany a  well-known  and  affable  gentleman  whose  name 
I  have  forgotten,  and  who  to  my  horror  asks  to  be  in- 
troduced to  some  one.  I  set  to  work  according  to 
Lichtenberg's  rule,  and  run  down  the  alphabet  in 
search  of  the  initial  letter  of  his  name.  A  vague  sym- 
pathy holds  me  at  the  letter  G.  Tentatively  I  add  the 
second  letter  and  am  arrested  at  e,  and  long  before  I 
have  tried  the  third  letter  r,  the  name  "Gerson"  sounds 
sonorously  upon  my  ear,  and  my  anguish  is  gone. 
While  taking  a  walk  I  meet  a  gentleman  from  whom 
I  receive  a  communication.  On  returning  home,  and 
in  attending  to  weightier  affairs,  the  matter  slips  my 
mind.  Moodily,  but  in  vain,  I  ransack  my  memory. 
Finally  I  observe  that  I  am  going  over  my  walk  again 
in  thought.  On  the  street  corner  in  question  the  self- 
same gentleman  stands  before  me  and  repeats  his 
communication.  In  this  process  are  successively  re- 
called to  consciousness  all  the  percepts  which  were 
connected  with  the  percept  that  was  lost,  and  with 
them,  finally,  that,  too,  is  brought  to  light.  In  the 
first  case — where  the  experience  had  already  been 
made  and  is  permanently  impressed  on  our  thought — 
a  systematic  procedure  is  both  possible  and  easy,  for 
we  know  that  a  name  must  be  composed  of  a  limited 
number  of  sounds.  But  at  the  same  time  it  should  be 
observed  that  the  labor  involved  in  such  a  combina- 


A  CCIDENT  IN  INVENTION  AND  DISCO  VER  Y.    *77 

torial  task  would  be  enormous  if  the  name  were  long 
and  the  responsiveness  of  the  mind  weaker. 

It  is  often  said,  and  not  wholly  without  justification, 
that  the  scientist  has  solved  a  riddle.  Every  problem 
in  geometry  may  be  clothed  in  the  garb  of  a  riddle. 
Thus  :  "What  thing  is  that  M  which  has  the  proper- 
ties A,  B,  C?"  "  What  circle  is  that  which  touches 
the  straight  lines  A,  J3,  but  touches  B  in  the  point  C?" 
The  first  two  conditions  marshal  before  the  imagina- 
tion the  group  of  circles  whose  centres  lie  in  the  line 
of  symmetry  of  A,  B.  The  third  condition  reminds 
us  of  all  the  circles  having  centres  in  the  straight  line 
that  stands  at  right  angles  to  B  in  C.  The  common 
term,  or  common  terms,  of  the  two  groups  of  images 
solves  the  riddle — satisfies  the  problem.  Puzzles  deal- 
ing with  things  or  words  induce  similar  processes,  but 
the  memory  in  such  cases  is  exerted  in  many  direc- 
tions and  more  varied  and  less  clearly  ordered  prov- 
inces of  ideas  are  surveyed.  The  difference  between 
the  situation  of  a  geometer  who  has  a  construction  to 
make,  and  that  of  an  engineer,  or  a  scientist,  con- 
fronted with  a  problem,  is  simply  this,  that  the  first 
moves  in  a  field  with  which  he  is  thoroughly  ac- 
quainted, whereas  the  two  latter  are  obliged  to  famil- 
iarise themselves  with  this  field  subsequently,  and  in 
a  measure  far  transcending  what  is  commonly  re- 
quired. In  this  process  the  mechanical  engineer  has 
at  least  always  a  definite  goal  before  him  and  definite 
means  to  accomplish  his  aim,  whilst  in  the  case  of  the 


278    ACCIDENT  IN  INVENTION  AND  DISCOVERY. 

scientist  that  aim  is  in  many  instances  presented  only 
in  vague  and  general  outlines.  Often  the  very  formu- 
lation of  the  riddle  devolves  on  him.  Frequently  it 
is  not  until  the  aim  has  been  reached  that  the  broader 
outlook  requisite  for  systematic  procedure  is  obtained. 
By  far  the  larger  portion  of  his  success,  therefore,  is 
contingent  on  luck  and  instinct.  It  is  immaterial,  so 
far  as  its  character  is  concerned,  whether  the  process 
in  question  is  brought  rapidly  to  a  conclusion  in  the 
brain  of  one  man,  or  whether  it  is  spun  out  for  cen- 
turies in  the  minds  of  a  long  succession  of  thinkers. 
The  same  relation  that  a  word  solving  a  riddle  bears 
to  that  riddle  is  borne  by  the  modern  conception  of 
light  to  the  facts  discovered  by  Grimaldi,  Romer, 
Huygens,  Newton,  Young,  Malus,  and  Fresnel,  and 
only  by  the  help  of  this  slowly  developed  conception 
is  our  mental  vision  enabled  to  embrace  the  broad 
domain  of  facts  in  question. 

A  welcome  complement  to  the  discoveries  which 
the  history  of  civilisation  and  comparative  psychology 
have  furnished,  is  to  be  found  in  the  confessions  of 
great  scientists  and  artists.  Scientists  and  artists,  we 
might  say,  for  Liebig  boldly  declared  there  was  no 
essential  difference  between  the  two.  Are  we  to  re- 
gard Leonardo  da  Vinci  as  a  scientist  or  as  an  artist? 
If  the  artist  builds  up  his  work  from  a  few  motives, 
the  scientist  discovers  the  motives  which  permeate 
reality.  If  scientists  like  Lagrange  or  Fourier  are  in 
a  certain  measure  artists  in  the  presentation  of  their 


ACCIDENT  IN  INVENTION  AND  DISCOVERY.    279 

results,  on  the  other  hand,  artists  like  Shakespeare  or 
Ruysdael  are  scientists  in  the  insight  which  must 
have  preceded  their  creations. 

Newton,  when  questioned  about  his  methods  of 
work,  could  give  no  other  answer  but  that  he  was 
wont  to  ponder  again  and  again  on  a  subject ;  and 
similar  utterances  are  accredited  to  D'Alembert  and 
Helmholtz.  Scientists  and  artists  both  recommend 
persistent  labor.  After  the  repeated  survey  of  a  field 
has  afforded  opportunity  for  the  interposition  of  ad- 
vantageous accidents,  has  rendered  all  the  traits  that 
suit  with  the  mood  or  the  dominant  thought  more 
vivid,  and  has  gradually  relegated  to  the  background 
all  things  that  are  inappropriate,  making  their  future 
appearance  impossible;  then  from  the  teeming,  swell- 
ing host  of  fancies  which  a  free  and  high-flown  im- 
agination calls  forth,  suddenly  that  particular  form 
arises  to  the  light  which  harmonises  perfectly  with 
the  ruling  idea,  mood,  or  design.  Then  it  is  that  that 
which  has  resulted  slowly  as  the  result  of  a  gradual 
selection,  appears  as  if  it  were  the  outcome  of  a  de- 
liberate act  of  creation.  Thus  are  to  be  explained  the 
statements  of  Newton,  Mozart,  Richard  Wagner,  and 
others,  when  they  say  that  thoughts,  melodies,  and 
harmonies  had  poured  in  upon  them,  and  that  they 
had  simply  retained  the  right  ones.  Undoubtedly, 
the  man  of  genius,  too,  consciously  or  instinctively, 
pursues  systematic  methods  wherever  it  is  possible ; 
but  in  his  delicate  presentiment  he  will  omit  many  a 


28o    ACCIDENT  IN  INVENTION  AND  DISCOVERY. 

task  or  abandon  it  after  a  hasty  trial  on  which  a  less 
endowed  man  would  squander  his  energies  in  'vain. 
Thus,  the  genius  accomplishes*  in  a  brief  space  of 
time  undertakings  for  which  the  life  of  an  ordinary 
man  would  far  from  suffice.  We  shall  hardly  go  astray 
if  we  regard  genius  as  only  a  slight  deviation  from 
the  average  mental  endowment — as  possessing  simply 
a  greater  sensitiveness  of  cerebral  reaction  and  a 
greater  swiftness  of  reaction.  The  men  who,  obeying 
their  inner  impulses,  make  sacrifices  for  an  idea  in- 
stead of  advancing  their  material  welfare,  may  appear 
to  the  full-blooded  Philistine  as  fools ;  yet  we  shall 
scarcely  adopt  Lombroso's  view,  that  genius  is  to  be 
regarded  as  a  disease,  although  it  is  unfortunately 
true  that  the  sensitive  brains  and  fragile  constitutions 
succumb  most  readily  to  sickness. 

The  remark  of  C.  G.  J.  Jacobi  that  mathematics 
is  slow  of  growth  and  only  reaches  the  truth  by  long 
and  devious  paths,  that  the  way  to  its  discovery  must 
be  prepared  for  long  beforehand,  and  that  then  the 
truth  will  make  its  long-deferred  appearance  as  if  im- 
pelled by  some  divine  necessity  f — all  this  holds  true 

*I  do  not  know  whether  Swift's  academy  of  schemers  in  Lagado,  in 
which  great  discoveries  and  inventions  were  made  by  a  sort  of  verbal  game 
of  dice,  was  intended  as  a  satire  on  Francis  Bacon's  method  of  making  dis- 
coveries by  means  of  huge  synoptic  tables  constructed  by  scribes.  It  cer- 
tainly would  not  have  been  ill-placed. 

t  "  Crescunt  disciplinae  lente  tardeque  ;  per  varies  errores  sero  perveni- 
tur  ad  veritatem.  Omnia  praeparata  esse  debent  diuturno  et  assiduo  labore 
ad  introitum  veritatis  novae.  Jam  ilia  certo  temporis  memento  divina  qua- 
darn  necessitate  coacta  emerget." 

Quoted  by  Simony,  In  tin  ringfOrmige*  Band  einen  Knottn  zu  machen, 
Vienna,  1881,  p.  41, 


A  CCIDENT  IN  INVENTION  AND  DISCO  VER  Y.    28 1 

of  every  science.  We  are  astounded  often  to  note 
that  it  required  the  combined  labors  of  many  eminent 
thinkers  for  a  full  century  to  reach  a  truth  which  it 
takes  us  only  a  few  hours  to  master  and  which  once 
acquired  seems  extremely  easy  to  reach  under  the 
right  sort  of  circumstances.  To  our  humiliation  we 
learn  that  even  the  greatest  men  are  born  more  for 
life  than  for  science.  The  extent  to  which  even  they 
are  indebted  to  accident — to  that  singular  conflux  of 
the  physical  and  the  psychical  life  in  which  the  con- 
tinuous but  yet  imperfect  and  never-ending  adaptation 
of  the  latter  to  the  former  finds  its  distinct  expression 
— that  has  been  the  subject  of  our  remarks  to-day. 
Jacobi's  poetical  thought  of  a  divine  necessity  acting 
in  science  will  lose  none  of  its  loftiness  for  us  if  we 
discover  in  this  necessity  the  same  power  that  de- 
stroys the  unfit  and  fosters  the  fit.  For  loftier,  nobler, 
and  more  romantic  than  poetry  is  the  truth  and  the 
reality. 


ON  SENSATIONS  OF  ORIENTATION.* 


'T^HROUGH  the  co-operation  of  a  succession  of  in- 
•*-  quirers,  among  whom  are  particularly  to  be  men- 
tioned Goltz  of  Strassburg  and  Breuer  of  Vienna, 
considerable  advances  have  been  made  during  the 
last  twenty-five  years  in  our  knowledge  of  the  means 
by  which  we  ascertain  our  position  in  space  and  the 
direction  of  our  motion,  or  orient  ourselves,  as  the 
phrase  goes.  I  presume  that  you  are  already  ac- 
quainted with  the  physiological  part  of  the  processes 
with  which  our  sensations  of  movement,  or,  more  gen- 
erally speaking,  our  sensations  of  orientation,  are  con- 
nected. Here  I  shall  consider  more  particularly  the 
physical  side  of  the  matter.  In  fact,  I  was  originally 
led  to  the  consideration  of  these  questions  by  the 
observation  of  extremely  simple  and  perfectly  well- 
known  physical  facts,  before  I  had  any  great  acquaint- 
ance with  physiology  and  while  pursuing  unbiasedly 
my  natural  thoughts ;  and  I  am  of  the  conviction  that 

*A  lecture  delivered  on  February  24,  1897,  before  the  Verein  zur   Ver- 
treitung  naturwissenschaftlicher  Kenntnisse  in  Wien. 


SENSATJONS  OF  ORIENTATION.  283 

the  way  which  I  have  pursued,  and  which  is  entirely 
free  from  hypotheses,  will,  if  you  will  follow  my  ex- 
position, be  that  of  easiest  acquisition  for  the  most  of 
you. 

No  man  of  sound  common  sense  could  ever  have 
doubted  that  a  pressure  or  force  is  requisite  to  set  a 
body  in  motion  in  a  given  direction  and  that  a  con- 
trary pressure  is  required  to  stop  suddenly  a  body  in 
motion.  Though  the  law  of  inertia  was  first  formu- 
lated with  anything  like  exactness  by  Galileo,  the 
facts  at  the  basis  of  it  were  known  long  previously  to 
men  of  the  stamp  of  Leonardo  da  Vinci,  Rabelais, 
and  others,  and  were  illustrated  by  them  with  appro- 
priate experiments.  Leonardo  knew  that  by  a  swift 
stroke  with  a  ruler  one  can  knock  out  from  a  vertical 
column  of  checkers  a  single  checker  without  over- 
throwing the  column.  The  experiment  with  a  coin 
resting  on  a  piece  of  pasteboard  covering  a  goblet, 
which  falls  into  the  goblet  when  the  pasteboard  is 
jerked  away,  like  all  experiments  of  the  kind,  is  cer- 
tainly very  old. 

With  Galileo  the  experience  in  question  assumes 
greater  clearness  and  force.  In  the  famous  dialogue 
on  the  Copernican  system  which  cost  him  his  free- 
dom, he  explains  the  tides  in  an  unfelicitous,  though 
in  principle  correct  manner,  by  the  analogue  of  a 
platter  of  water  swung  to  and  fro.  In  opposition  to 
the  Aristotelians  of  his  time,  who  believed  the  des- 


284  SENSATIONS  OF  ORIENTATION. 

cent  of  a  heavy  body  could  be  accelerated  by  the 
superposition  of  another  heavy  body,  he  asserted  that 
a  body  could  never  be  accelerated  by  one  lying  upon 
it  unless  the  first  in  some  way  impeded  the  super- 
posed body  in  its  descent.  To  seek  to  press  a  falling 
body  by  means  of  another  placed  upon  it,  is  as  sense- 
less as  trying  to  prod  a  man  with  a  lance  when  the  man 
is  speeding  away  from  one  with  the  same  velocity  as 
the  lance.  Even  this  little  excursion  into  physics  can 
explain  much  to  us.  You  know  the  peculiar  sensation 
which  one  has  in  falling,  as  when  one  jumps  from  a 
high  springboard  into  the  water,  and  which  is  also 
experienced  in  some  measure  at  the  beginning  of  the 
descent  of  elevators  and  swings.  The  reciprocal  grav- 
itational pressure  of  the  different  parts  of  our  body, 
which  is  certainly  felt  in  some  manner,  vanishes  in 
free  descent,  or,  in  the  case  of  the  elevator,  is  dimin- 
ished on  the  beginning  of  the  descent.  A  similar  sen- 
sation would  be  experienced  if  we  were  suddenly 
transported  to  the  moon  where  the  acceleration  of 
gravity  is  much  less  than  upon  the  earth.  I  was  led 
to  these  considerations  in  1866  by  a  suggestion  in 
physics,  and  having  also  taken  into  account  the  alter- 
ations of  the  blood-pressure  in  the  cases  in  question, 
I  found  I  coincided  without  knowing  it  with  Wollaston 
and  Purkinje.  The  first  as  early  as  1810  in  his  Croo- 
nian  lecture  had  touched  on  the  subject  of  sea-sick- 
ness and  explained  it  by  alterations  of  the  blood-pres- 


SENSATIONS  OF  ORIENTATION.  285 

sure,  and  later  had  laid  similar  considerations  at  the 
basis  of  his  explanation  of  vertigo  (1820-1826).* 

Newton  was  the  first  to  enunciate  with  perfect 
generality  that  a  body  can  change  the  velocity  and 
direction  of  its  motion  only  by  the  action  of  a  force, 
or  the  action  of  a  second  body.  A  corollary  of  this 
law  which  was  first  expressly  deduced  by  Euler  is 
that  a  body  can  never  be  set  rotating  or  made  to  cease 
rotating  of  itself  but  only  by  forces  and  other  bodies. 
For  example,  turn  an  open  watch  which  has  run  down 
freely  backwards  and  forwards  in  your  hand.  The 
balance-wheel  will  not  fully  catch  the  rapid  rotations, 
it  does  not  even  respond  fully  to  the  elastic  force  of 
the  spring  which  proves  too  weak  to  carry  the  wheel 
entirely  with  it. 

Let  us  consider  now  that  whether  we  move  our- 
selves by  means  of  our  legs,  or  whether  we  are 
moved  by  a  vehicle  or  a  boat,  at  first  only  a  part 
of  our  body  is  directly  moved  and  the  rest  of  it  is 
afterwards  set  in  motion  by  the  first  part.  We  see 
that  pressures,  pulls,  and  tensions  are  always  pro- 
duced between  the  parts  of  the  body  in  this  action, 
which  pressures,  pulls,  and  tensions  give  rise  to  sen- 
sations by  which  the  forward  or  rotary  movements  in 
which  we  are  engaged  are  made  perceptible.!  But  it 

*  Wollaston,  Philosophical  Transactions,  Royal  Society,  1810.  In  the  same 
place  Wollaston  also  describes  and  explains  the  creaking  of  the  muscles. 
My  attention  was  recently  called  to  this  work  by  Dr.  W.  Pascheles.-Cf.  also 
Purkinje,  Prager  medicin.  Jahrbttcher,  Bd.  6,  Wien,  1820. 

t  Similarly  many  external  forces  do  not  act  at  once  on  all  part*  of  the 
earth,  and  the  internal  forces  which  produce  deformations  act  at  first  imme- 


286 


SENSATIONS  OF  ORIENTATION. 


is  quite  natural  that  sensations  so  familiar  should  be 
little  noticed  and  that  attention  should  be  drawn  to 
them  only  under  special  circumstances  when  they  oc- 
cur unexpectedly  or  with  unusual  strength. 

Thus  my  attention  was  drawn  to  this  point  by  the 
sensation  of  falling  and  subsequently  by  another  sin- 
gular occurrence.  I  was  rounding  a  sharp  railway 
curve  once  when  I  suddenly  saw  all  the  trees,  houses, 


LJ 

Fig.  45- 

and  factory  chimneys  along  the  track  swerve  from  the 
vertical  and.  assume  a  strikingly  inclined  position. 
What  had  hitherto  appeared  to  me  perfectly  natural, 
namely,  the  fact  that  we  distinguish  the  vertical  so 
perfectly  and  sharply  from  every  other  direction,  now 

diately  only  upon  limited  parts.  If  the  earth  were  a  feeling  being,  the  tides 
and  other  terrestrial  events  would  provoke  in  it  similar  sensations  to  those 
of  our  movements.  Perhaps  the  slight  alterations  of  the  altitude  of  the 

slight  deformations  of  the  central  ellipsoid  occasioned  by  seismical  happen- 
ings. 


SENSATIONS  OF  ORIENTATION.  287 

struck  me  as  enigmatical.  Why  is  it  that  the  same 
direction  can  now  appear  vertical  to  me  and  now  can- 
not? By  what  is  the  vertical  distinguished  for  us? 
(Compare  Figure  45.) 

The  rails  are  raised  on  the  convex  or  outward  side 
of  the  track  in  order  to  insure  the  stability  of  the  car- 
riage as  against  the  action  of  the  centrifugal  force,  the 
whole  being  so  arranged  that  the  combination  of  the 
force  of  gravity  with  the  centrifugal  force  of  the  train 
shall  give  rise  to  a  force  perpendicular  to  the  plane 
of  the  rails. 

Let  us  assume,  now,  that  under  all  circumstances 
we  somehow  sense  the  direction  of  the  total  resultant 
mass-acceleration  whencesoever  it  may  arise  as  the 
vertical.  Then  both  the  ordinary  and  the  extraor- 
dinary phenomena  will  be  alike  rendered  intelligible.* 

I  was  now  desirous  of  putting  the  view  I  had 
reached  to  a  more  convenient  and  exact  test  than  was 
possible  on  a  railway  journey  where  one  has  no  con- 
trol over  the  determining  circumstances  and  cannot 
alter  them  at  will.  I  accordingly  had  the  simple  ap- 
paratus constructed  which  is  represented  in  Figure  46. 

In  a  large  frame  BB,  which  is  fastened  to  the  walls, 
rotates  about  a  vertical  axis  A  A  a  second  frame  RR, 
and  within  the  latter  a  third  one  rr,  which  can  be  set 


*  For  the  popular  explanation  by  unconscious  inference  the  matter  is  ex- 
tremely simple.  We  regard  the  railway  carriage  as  vertical  and  unconsciously 
infer  the  inclination  of  the  trees.  Of  course  the  opposite  conclusion  that  we 
regard  the  trees  as  vertical  and  infer  the  inclination  of  the  carriage,  unfort- 
unately, is  equally  clear  on  this  theory. 


288 


SENS  A  T1ONS  OF  ORIENTA  TION. 


at  any  distance  and  position  from  the  axis,  made  sta- 
tionary or  movable,  and  is  provided  with  a  chair  for 
the  observer. 

The  observer  takes  his  seat  in  the  chair  and  to 
prevent  disturbances  of  judgment  is  enclosed  in  a  pa- 
per box.  If  the  observer  together  with  the  frame  rr 
be  then  set  in  uniform  rotation,  he  will  feel  and  see 
the  beginning  of  the  rotation  both  as  to  direction  and 


Fig.  45. 
From  Mach's  Bewegungsemffindungen,  Leipsic,  Engelmann,  1875. 

amount  very  distinctly  although  every  outward  visible 
or  tangible  point  of  reference  is  wanting.  If  the  mo- 
tion be  uniformly  continued  the  sensation  of  rotation 
will  gradually  cease  entirely  and  the  observer  will  im- 
agine himself  at  rest.  But  if  rr  be  placed  outside  the 
axis  of  rotation,  at  once  on  the  rotation  beginning,  a 
strikingly  apparent,  palpable,  actually  visible  inclina- 
tion of  the  entire  paper  box  is  produced,  slight  when 


SENSATIONS  OF  ORIENTATION.  289 

the  rotation  is  slow,  strong  when  the  rotation  is  rapid, 
and  continuing  as  long  as  the  rotation  lasts.  It  is  ab- 
solutely impossible  for  the  observer  to  escape  perceiv- 
ing the  inclination,  although  here  also  all  outward 
points  of  reference  are  wanting.  If  the  observer,  for 
example,  is  seated  so  as  to  look  towards  the  axis,  he 
will  feel  the  box  strongly  tipped  backwards,  as  it  nec- 
essarily must  be  if  the  direction  of  the  total  resultant 
force  is  perceived  as  the  vertical.  For  other  positions 
of  the  observer  the  situation  is  similar.* 

Once,  while  performing  one  of  these  experiments, 
and  after  rotating  so  long  that  I  was  no  longer  con- 
scious of  the  movement,  I  suddenly  caused  the  ap- 
paratus to  be  stopped,  whereupon  I  immediately  felt 
and  saw  myself  with  the  whole  box  rapidly  flung  round 
in  rotation  in  the  opposite  direction,  although  I  knew 
that  the  whole  apparatus  was  at  rest  and  every  out- 
ward point  of  reference  for  the  perception  of  motion 
was  wanting.  Every  one  who  disbelieves  in  sensa- 
tions of  movement  should  be  made  acquainted  with 
these  phenomena.  Had  Newton  known  them  and  had 
he  ever  observed  how  we  may  actually  imagine  our 
selves  turned  and  displaced  in  space  without  the  as- 
sistance of  stationary  bodies  as  points  of  reference,  he 
would  certainly  have  been  confirmed  more  than  ever 


*  It  will  be  observed  that  my  way  of  thinking  and  experimenting  here  is 
related  to  that  which  led  Knight  to  the  discovery  and  investigation  of  the 
geotropism  of  plants.  Philosophical  Transactions,  January  9,  1806.  The  rela- 
tions between  vegetable  and  animal  geotropism  have  been  more  recently  in- 
vestigated  by  J.  Loeb. 


2QO  SENSATIONS  OF  ORIENTATION. 

in  his  unfortunate  speculations  regarding  absolute 
space. 

The  sensation  of  rotation  in  the  opposite  direction 
after  the  apparatus  has  been  stopped,  slowly  and  grad- 
ually ceases.  But  on  accidentally  inclining  my  head 
once  during  this  occurrence,  the  axis  of  apparent  ro- 
tation was  also  observed  to  incline  in  exactly  the  same 
manner  both  as  to  direction  and  as  to  amount.  It  is 
accordingly  clear  that  the  acceleration  or  retardation 
of  rotation  is  felt.  The  acceleration  operates  as  a 
stimulus.  The  sensation,  however,  like  almost  all 
sensations,  though  it  gradually  decreases,  lasts  per- 
ceptibly longer  than  the  stimulus.  Hence  the  long 
continued  apparent  rotation  after  the  stopping  of  the 
apparatus.  The  organ,  however,  which  causes  the 
persistence  of  this  sensation  must  have  its  seat  in  the 
head,  since  otherwise  the  axis  of  apparent  rotation 
could  not  assume  the  same  motion  as  the  head. 

If  I  were  to  say,  now,  that  a  light  had  flashed 
upon  me  in  making  these  last  observations,  the  ex- 
pression would  be  a  feeble  one.  I  ought  to  say  I  ex- 
perienced a  perfect  illumination.  My  juvenile  expe- 
riences of  vertigo  occurred  to  me.  I  remembered 
Flourens's  experiments  relative  to  the  section  of  the 
semi-circular  canals  of  the  labyrinths  of  doves  and 
rabbits,  where  this  inquirer  had  observed  phenomena 
similar  to  vertigo,  but  which  he  preferred  to  interpret, 
from  his  bias  to  the  acoustic  theory  of  the  labyrinth, 
as  the  expression  of  painful  auditive  disturbances.  I 


SENSATIOA'S  OF  ORIENTATION.  291 

saw  that  Goltz  had  nearly  but  not  quite  hit  the  bull's 
eye  with  his  theory  of  the  semi-circular  canals.  This 
inquirer,  who,  from  his  happy  habit  of  following  his 
own  natural  thoughts  without  regard  for  tradition, 
has  cleared  up  so  much  in  science,  spoke,  as  early  as 
1870,  on  the  ground  of  experiments,  as  follQws  :  "It 
is  uncertain  whether  the  semi-circular  canals  are  aud- 
itive organs  or  not.  In  any  event  they  form  an  appa- 
ratus which  serves  for  the  preservation  of  equilibrium. 
They  are,  so  to  speak,  the  sense-organs  of  equilib- 
rium of  the  head  and  indirectly  of  the  whole  body."  I 
remembered  the  galvanic  dizziness  which  had  been 
observed  by  Ritter  and  Purkinje  on  the  passage  of  a 
current  through  the  head,  when  the  persons  experi- 
mented upon  imagined  they  were  falling  towards  the 
cathode.  The  experiment  was  immediately  repeated, 
and  sometime  later  (1874)  I  was  enabled  to  demon- 
strate the  same  objectively  with  fishes,  all  of  which 
placed  themselves  sidewise  and  in  the  same  direction 
in  the  field  of  the  current  as  if  at  command.*  Miil- 
ler's  doctrine  of  specific  energies  now  appeared  to  me 
to  bring  all  these  new  and  old  observations  into  a  sim- 
ple, connected  unity. 

Let  us  picture  to  ourselves  the  labyrinth  of  the 
ear  with  its  three  semi-circular  canals  lying  in  three 
mutually  perpendicular  planes  (Comp.  Fig.  47),  the 

*This  experiment  is  doubtless  related  to  the  galvanotropic  experiment 
with  the  larva  of  frogs  described  ten  years  later  by  L.  Hermann.  Compare 
on  this  point  my  remarks  in  the  Anzeigcr  der  U'ientr  Akademie,  1886.  No.  91. 
Recent  experiments  in  galvanotropism  are  due  to  J.  Loeb. 


292  SENS  A  TIONS  OF  ORIENT  A  TION. 

mysterious  position  of  which  inquirers  have  endeav- 
ored to  explain  in  every  possible  and  impossible  way. 
Let  us  conceive  the  nerves  of  the  ampullae,  or  the  di- 
lated extensions  of  the  semi- circular  canals,  equipped 
with  a  capacity  for  responding  to  every  imaginable 
stimulus  with  a  sensation  of  rotation  just  as  the  nerves 
of  the  retina  of  the  eye  when  excited  by  pressures, 


Fig.  47- 

The  labyrinth  of  a  dove  (stereoscopically  reproduced),  from  R.  Ewald, 
Nervuf  Octavus,  Wiesbaden,  Bergmann,  1892. 

by  electrical  or  chemical  stimuli  always  respond  with 
the  sensation  of  light ;  let  us  picture  to  ourselves, 
further,  that  the  usual  excitation  of  the  ampullae 
nerves  is  produced  by  the  inertia  of  the  contents  of 
the  semi-circular  canals,  which  contents  on  suitable 
rotations  in  the  plane  of  the  semi-circular  canal  are 
left  behind  in  the  motion,  or  at  least  have  a  tendency 


SENS  A  TIONS  OF  ORIENT  A  TION.  293 

to  remain  behind  and  consequently  exert  a  pressure. 
It  will  be  seen  that  on  this  supposition  all  the  single 
facts  which  without  the  theory  appear  as  so  many 
different  individual  phenomena,  become  from  this  sin- 
gle point  of-view  clear  and  intelligible. 

I  had  the  satisfaction,  immediately  after  the  com- 
munication in  which  I  set  forth  this  idea,*  of  seeing  a 
paper  by  Breuer  appear  f  in  which  this  author  had 
arrived  by  entirely  different  methods  at  results  that 
agreed  in  all  essential  points  with  my  own.  A  few 
weeks  later  appeared  the  researches  of  Crum  Brown 
of  Edinburgh,  whose  methods  were  even  still  nearer 
mine.  Breuer's  paper  was  far  richer  in  physiologi- 
cal respects  than  mine,  and  he  had  particularly  gone 
into  greater  detail  in  his  investigation  of  the  collat- 
eral effects  of  the  reflex  motions  and  orientation  of 
the  eyes  in  the  phenomena  under  consideration.  \  In 
addition  certain  experiments  which  I  had  suggested  in 
my  paper  as  a  test  of  the  correctness  of  the  view 
in  question  had  already  been  performed  by  Breuer. 
Breuer  has  also  rendered  services  of  the  highest  order 
in  the  further  elaboration  of  this  field.  But  in  a 
physical  regard,  my  paper  was,  of  course,  more  com- 
plete. 

In  order  to  portray  to  the  eye  the  behavior  of  the 
semi-circular  canals,  I  have  constructed  here  a  little 

*  Wiener  Akad.,  6  November,  1873. 
t  Wiener  Gesellschaft  der  Aerzte,  14  November.  1874. 

\\  have  made  a  contribution  to  this  last  question  in  my  Analjru't  of  tkt 
Sensations,  (1886),  English  translation,  1897. 


294 


SENS  A  TIONS  OF  ORIENTA  TION. 


apparatus.  (S*ee  Fig.  48.)  The  large  rotatable  disc 
represents  the  osseous  semi-circular  canal,  which  is 
continuous  with  the  bones  of  the  head  ;  the  small  disc, 
which  is  free  to  rotate  on  the  axis  of  the  first,  repre- 
sents the  mobile  and  partly  liquid  contents  of  the  semi- 
circular canal.  On  rotating  the  large  disc,  the  small 

disc  as  you  see  re- 
mains  behind.  I 
have  to  turn  some 
time  before  the 
small  disc  is  carried 
along  with  the  large 
one  by  friction.  But 
if  I  now  stop  the 
large  disc  the  small 
disc  as  you  see  con- 
tinues to  rotate. 

Simply  assume 
now  that  the  rota- 
tion of  the  small 
disc,  say  in  the  di- 
rection of  the  hands 
of  a  watch,  would 
give  rise  to  a  sensation  of  rotation  in  the  opposite 
direction,  and  conversely,  and  you  already  under- 
stand a  good  portion  of  the  facts  above  set  forth. 
The  explanation  still  holds,  even  if  the  small  disc 
does  not  perform  appreciable  rotations  but  is  checked 
by  a  contrivance  similar  to  an  elastic  spring,  the  ten- 


Fig.  48. 

Model  representing  the  action  of  the  semi- 
circular canals. 


SENSATIONS  OF  ORIENTATION.  395 

sion  of  which  disengages  a  sensation.  Conceive,  now, 
three  such  contrivances  with  their  mutually  perpen- 
dicular planes  of  rotation  joined  together  so  as  to 
form  a  single  apparatus;  then  to  this  apparatus  as  a 
whole,  no  rotation  can  be  imparted  without  its  being 
indicated  by  the  small  mobile  discs  or  by  the  springs 
which  are  attached  to  them.  Conceive  both  the  right 
and  the  left  ear  equipped  with  such  an  apparatus,  and 
you  will  find  that  it  answers  all  the  purposes  of  the 
semi-circular  canals,  which  you  see  represented  ste- 
reoscopically  in  Fig.  47  for  the  ear  of  a  dove. 

Of  the  many  experiments  which  I  have  made  on 
my  own  person,  and  the  results  of  which  could  be 
predicted  by  the  new  view  according  to  the  behavior 
of  the  model  and  consequently  according  to  the  rules 
of  mechanics,  I  shall  cite  but  one.  I  fasten  a  horizon- 
tal board  in  the  frame  RR  of  my  rotatory  apparatus, 
lie  down  upon  the  same  with  my  right  ear  upon  the 
board,  and  cause  the  apparatus  to  be  uniformly  ro- 
tated. As  soon  as  I  no  longer  perceive  the  rotation, 
I  turn  around  upon  my  left  ear  and  immediately  the 
sensation  of  rotation  again  starts  up  with  marked  viv- 
idness. The  experiment  can  be  repeated  as  often  as 
one  wishes.  A  slight  turn  of  the  head  even  is  suffi- 
cient for  reviving  the  sensation  of  rotation  which  in 
the  perfectly  quiescent  state  at  once  disappears  alto- 
gether. 

We  will  imitate  the  experiment  on  the  model.  I 
turn  the  large  disc  until  finally  the  small  disc  is  car- 


296  SENSATIONS  OF  ORIENTATION. 

ried  along  with  it.  If,  now,  while  the  rotation  con- 
tinues uniform,  I  burn  off  a  little  thread  which  you 
see  here,  the  small  disc  will  be  flipped  round  by  a 
spring  into  its  own  plane  180°,  so  as  now  to  present 
its  opposite  side  to  you,  when  the  rotation  at  once  be- 
gins in  the  opposite  direction. 

We  have  consequently  a  very  simple  means  for  de- 
termining whether  one  is  actually  the  subject  or  not 
of  uniform  and  imperceptible  rotations.  If  the  earth 
rotated  much  more  rapidly  than  it  really  does,  or  if 
our  semi-circular  canals  were  much  more  sensitive,  a 
Nansen  sleeping  at  the  North  Pole  would  be  waked 
by  a  sensation  of  rotation  every  time  he  turned  over. 
Foucault's  pendulum  experiment  as  a  demonstration 
of  the  earth's  rotation  would  be  superfluous  under 
such  circumstances.  The  only  reason  we  cannot  prove 
the  rotation  of  the  earth  with  the  help  of  our  model, 
lies  in  the  small  angular  velocity  of  the  earth  and  in 
the  consequent  liability  to  great  experimental  errors.* 
Aristotle  has  said  that  "The  sweetest  of  all 
things  is  knowledge."  And  he  is  right.  But  if  you 
were  to  suppose  that  the  publication  of  a  new  view 
were  productive  of  unbounded  sweetness,  you  would 
be  mightily  mistaken.  No  one  disturbs  his  fellow-men 
with  a  new  view  unpunished.  Nor  should  the  fact  be 
\  made  a  subject  of  reproach  to  these  fellow-men.  To 

*In  my  Grundlinien  der  Lehre  von  den  Bewegvngsempfindungen,  1875, 
the  matter  occupying  lines  4  to  13  of  page  ao  from  below,  which  rests  on  an 
error,  is,  as  I  have  also  elsewhere  remarked,  to  be  stricken  out.  For  another 
experiment  related  to  that  of  Foucault,  compare  my  Mechanics,  p.  303. 


SENSATIONS  OF  ORIENTATION.  397 

presume  to  revolutionise  the  current  way  of  thinking 
with  regard  to  any  question,  is  no  pleasant  task,  and 
above  all  not  an  easy  one.  They  who  have  advanced 
new  views  know  best  what  serious  difficulties  stand  in 
their  way.  With  honest  and  praiseworthy  zeal,  men 
set  to  work  in  search  of  everything  that  does  not 
suit  with  them.  They  seek  to  discover  whether  they 
cannot  explain  the  facts  better  or  as  well,  or  approxi- 
mately as  well,  by  the  traditional  views.  And  that, 
too,  is  justified.  But  at  times  some  extremely  artless 
animadversions  are  heard  that  almost  nonplus  us. 
"If  a  sixth  sense  existed  it  could  not  fail  to  have 
been  discovered  thousands  of  years  ago."  Indeed; 
there  was  a  time,  then,  when  only  seven  planets  could 
have  existed!  But  I  do  not  believe  that  any  one  will 
lay  any  weight  on  the  philological  question  whether 
the  set  of  phenomena  which  we  have  been  considering 
should  be  called  a  sense.  The  phenomena  will  not 
disappear  when  the  name  disappears.  It  was  further 
said  to  me  that  animals  exist  which  have  no  labyrinth, 
but  which  can  yet  orientate  themselves,  and  that  con- 
sequently the  labyrinth  has  nothing  to  do  with  orien- 
tation. We  do  not  walk  forsooth  with  our  legs,  be- 
cause snakes  propel  themselves  without  them  ! 

But  if  the  promulgator  of  a  new  idea  cannot  hope 
for  any  great  pleasure  from  its  publication,  yet  the 
critical  process  which  his  views  undergo  is  extremely 
helpful  to  the  subject-matter  of  them.  All  the  defects 
which  necessarily  adhere  to  the  new  view  are  gradu- 


298  SENSATIONS  OF  ORIENTATION. 

ally  discovered  and  eliminated.  Over-rating  and  ex- 
aggeration give  way  to  more  sober  estimates.  And 
so  it  came  about  that  it  was  found  unpermissible  to 
attribute  all  functions  of  orientation  exclusively  to  the 
labyrinth.  In  these  critical  labors  Delage,  Aubert, 
Breuer,  Ewald,  and  others  have  rendered  distin- 
guished services.  It  can  also  not  fail  to  happen  that 
fresh  facts  become  known  in  this  process  which  could 
have  been  predicted  by  the  new  view,  which  actually 
were  predicted  in  part,  and  which  consequently  fur- 
nish a  support  for  the  new  view.  Breuer  and  Ewald 
succeeded  in  electrically  and  mechanically  exciting 
the  labyrinth,  and  even  single  parts  of  the  labyrinth, 
and  thus  in  producing  the  movements  that  belong  to 
such  stimuli.  It  was  shown  that  when  the  semi-circu- 
lar canals  were  absent  vertigo  could  not  be  produced, 
when  the  entire  labyrinth  was  removed  the  orienta- 
tion of  the  head  was  no  longer  possible,  that  without 
the  labyrinth  galvanic  vertigo  could  not  be  induced.  I 
myself  constructed  as  early  as  1875  an  apparatus  for 
observing  animals  in  rotation,  which  was  subsequently 
reinvented  in  various  forms  and  has  since  received  the 
name  of  "cyclostat."*  In  experiments  with  the  most 
varied  kinds  of  animals  it  was  shown  that,  for  exam- 
ple, the  larvae  of  frogs  are  not  subject  to  vertigo  until 
their  semi-circular  canals  which  at  the  start  are  want- 
ing are  developed  (K.  Schafer).  A  large  percentage 
of  the  deaf  and  dumb  are  afflicted  with  grave  affec- 

*Anteiger  der  Wiener  Akad.,  30  December,  1875. 


SENSATIONS  OF  ORIENTATION.  299 

tions  of  the  labyrinth.  The  American  psychologist, 
William  James,  has  made  whirling  experiments  with 
many  deaf  and  dumb  subjects,  and  in  a  large  number 
of  them  found  that  susceptibility  to  giddiness  is  want- 
ing. He  also  found  that  many  deaf  and  dumb  people 
on  being  ducked  under  water,  whereby  they  lose  their 
weight  and  consequently  have  no  longer  the  full  as- 
sistance of  their  muscular  sense,  utterly  lose  their 
sense  of  position  in  space,  do  not  know  which  is  up 
and  which  is  down,  and  are  thrown  into  the  greatest 
consternation, — results  which  do  not  occur  in  normal 
men.  Such  facts  are  convincing  proof  that  we  do  not 
orientate  ourselves  entirely  by  means  of  the  labyrinth, 
important  as  it  is  for  us.  Dr.  Kreidl  has  made  ex- 
periments similar  to  those  of  James  and  found  that 
not  only  is  vertigo  absent  in  deaf  and  dumb  people 
when  whirled  about,  but  that  also  the  reflex  move- 
ments of  the  eyes  which  are  normally  induced  by  the 
labyrinth  are  wanting.  Finally,  Dr.  Pollak  has  found 
that  galvanic  vertigo  does  not  exist  in  a  large  per- 
centage of  the  deaf  and  dumb.  Neither  the  jerking 
movements  nor  the  uniform  movements  of  the  eyes 
were  observed  which  normal  human  beings  exhibit  in 
the  Ritter  and  Purkinje  experiment. 

After  the  physicist  has  arrived  at  the  idea  that  the 
semi-circular  canals  are  the  organ  of  sensation  of  ro- 
tation or  of  angular  acceleration,  he  is  next  con- 
strained to  ask  for  the  organs  that  mediate  the  sensa- 
tion of  acceleration  noticed  in  forward  movements. 


300  SENSATIONS  OF  ORIENTATION. 

In  searching  for  an  organ  for  this  function,  he  of 
course  is  not  apt  to  select  one  that  stands  in  no  ana- 
tomical and  spatial  relation  with  the  semi- circular 
canals.  And  in  addition  there  are  physiological  con- 
siderations to  be  weighed.  The  preconceived  opinion 
once  having  been  abandoned  that  the  entire  labyrinth 
is  auditory  in  its  function,  there  remains  after  the 
cochlea  is  reserved  for  sensations  of  tone  and  the 
semi-circular  canals  for  the  sensation  of  angular  ac- 
celeration, the  vestibule  for  the  discharge  of  additional 
functions.  The  vestibule,  particularly  the  part  of  it 
known  as  the  sacculus,  appeared  to  me,  by  reason  of 
the  so-called  otoliths  which  it  contains,  eminently 
adapted  for  being  the  organ  of  sensation  of  forward 
acceleration  or  of  the  position  of  the  head.  In  this 
conjecture  I  again  closely  coincided  with  Breuer. 

That  a  sensation  of  position,  of  direction  and 
amount  of  mass-acceleration  exists,  our  experience  in 
elevators  as  well  as  of  movement  in  curved  paths  is 
sufficient  proof.  I  have  also  attempted  to  produce  and 
destroy  suddenly  great  velocities  of  forward  move- 
ment by  means  of  various  contrivances  of  which  I 
shall  mention  only  one  here.  If,  while  enclosed  in 
the  paper  box  of  my  large  whirling  apparatus  at  some 
distance  from  the  axis,  my  body  is  in  uniform  rotation 
which  I  no  longer  feel,  and  I  then  loosen  the  connex- 
ions of  the  frame  rr  with  R  thus  making  the  former 
moveable  and  I  then  suddenly  stop  the  larger  frame, 
my  forward  motion  is  abruptly  impeded  while  the 


SENSATIONS  OF  ORIENTATION.  ^01 

frame  rr  continues  to  rotate.  I  imagine  now  that  I 
am  speeding  on  in  a  straight  line  in  a  direction  oppo- 
site to  that  of  the  checked  motion.  Unfortunately,  for 
many  reasons  it  cannot  be  proved  convincingly  that 
the  organ  in  question  has  its  seat  in  the  head.  Ac- 
cording to  the  opinion  of  Delage,  the  labyrinth  has 
nothing  to  do  with  this  particular  sensation  of  move- 
ment. Breuer,  on  the  other  hand,  is  of  the  opinion 
that  the  organ  of  forward  movement  in  man  is  stunted 
and  the  persistence  of  the  sensation  in  question  is  too 
brief  to  permit  our  instituting  experiments  as  obvious 
as  in  the  case  of  rotation.  In  fact,  Crum  Brown  once 
observed  while  in  an  irritated  condition  peculiar  ver- 
tigal  phenomena  in  his  own  person,  which  were  all 
satisfactorily  explained  by  an  abnormally  long  persist- 
ence of  the  sensation  of  rotation,  and  I  myself  in  an 
analogous  case  on  the  stopping  of  a  railway  train  felt 
the  apparent  backward  motion  in  striking  intensity 
and  for  an  unusual  length  of  time. 

There  is  no  doubt  whatever  that  we  feel  changes 
of  vertical  acceleration,  and  it  will  appear  from  the 
following  extremely  probable  that  the  otoliths  of  the 
vestibule  are  the  sense-organ  for  the  direction  of  the 
mass-acceleration.  It  will  then  be  incompatible  with 
a  really  logical  view  to  regard  the  latter  as  incapable 
of  sensing  horizontal  accelerations. 

In  the  lower  animals  the  analogue  of  the  labyrinth 
is  shrunk  to  a  little  vesicle  filled  with  a  liquid  and 
containing  tiny  crystals,  auditive  stones,  or  otoliths,  of 


302  SENSATIONS  OF  ORIENTATION. 

greater  specific  gravity,  suspended  on  minute  hairs. 
These  crystals  appear  physically  well  adapted  for  in- 
dicating both  the  direction  of  gravity  and  the  direction 
of  incipient  movements.  That  they  discharge  the  for- 
mer function,  Delage  was  the  first  to  convince  himself 
by  experiments  with  lower  animals  which  on  the  re- 
moval of  the  otoliths  utterly  lost  their  bearings  and 
could  no  longer  regain  their  normal  position.  Loeb 
also  found  that  fishes  without  labyrinths  swim  now  on 
their  bellies  and  now  on  their  backs.  But  the  most 
remarkable,  most  beautiful,  and  most  convincing  ex- 
periment is  that  which  Dr.  Kreidl  instituted  with 
crustaceans.  According  to  Hensen,  certain  Crustacea 
on  sloughing  spontaneously  introduce  fine  grains  of 
sand  as  auditive  stones  into  their  otolith  vesicle.  At 
the  ingenious  suggestion  of  S.  Exner,  Dr.  Kreidl  con- 
strained some  of  these  animals  to  put  up  with  iron 
filings  {fcrrum  limatum).  If  the  pole  of  an  electro- 
magnet be  brought  near  the  animal,  it  will  at  once 
turn  its  back  away  from  the  pole  accompanying  the 
movement  with  appropriate  reflex  motions  of  the  eye 
the  moment  the  current  is  closed,  exactly  as  if  grav- 
ity had  been  brought  to  bear  upon  the  animal  in  the 
same  direction  as  the  magnetic  force.*  This,  in  fact, 
is  what  should  be  expected  from  the  function  ascribed 
to  the  otoliths.  If  the  eyes  be  covered  with  asphalt 

*The  experiment  was  specially  interesting  for  me  as  I  had  already  at- 
tempted in  1874,  although  with  very  little  confidence  and  without  success,  to 
excite  electromagnetically  my  own  labyrinth  through  which  I  had  caused  a 
current  to  pass. 


SENSATIONS  OF  ORIENTATION,  303 

varnish,  and  the  auditive  sacs  removed,  the  crusta- 
ceans lose  their  sense  of  direction  utterly,  tumble 
head  over  heels,  lie  on  their  side  or  their  back  in- 
differently. This  does  not  happen  when  the  eyes  only 
are  covered.  For  vertebrates,  Breuer  has  demon- 
strated by  searching  investigations  that  the  otoliths, 
or  better,  statoliths,  slide  in  three  planes  parallel  to 
the  planes  of  the  semi-circular  canals,  and  are  con- 
sequently perfectly  adapted  for  indicating  changes 
both  in  the  amount  and  the  direction  of  the  mass- 
acceleration.* 

I  have  already  remarked  that  not  every  function 
of  orientation  can  be  ascribed  exclusively  to  the  laby- 
rinth. The  deaf  and  dumb  who  have  to  be  immersed 
in  water,  and  the  crustaceans  who  must  have  their 
eyes  closed  if  they  are  to  be  perfectly  disorientated,  are 
proof  of  this  fact.  I  saw  a  blind  cat  at  Hering's  lab- 
oratory which  to  one  who  was  not  a  very  attentive  ob- 
server behaved  exactly  like  a  seeing  cat.  It  played 
nimbly  with  objects  rolling  on  the  floor,  stuck  its  head 
inquisitively  into  open  drawers,  sprang  dexterously 
upon  chairs,  ran  with  perfect  accuracy  through  open 


*  Perhaps  the  discussion  concerning  the  peculiarity  of  cats  always  falling 
on  their  feet,  which  occupied  the  Parisian  Academy,  and,  incidentally,  Pa- 
risian society  a  few  years  ago,  will  be  remembered  here.  I  believe  that  the 
questions  which  arose  are  disposed  of  by  the  consideratfons  advanced  in  my 
Beviegungsempfindungen  (1875).  I  also  partly  gave,  as  early  as  1866,  the  ap- 
paratus conceived  by  the  Parisian  scientists  to  illustrate  the  phenomena  In 
question.  One  difficulty  was  left  untouched  in  the  Parisian  debate.  The 
otolith  apparatus  of  the  cat  can  render  it  no  service  in  free  descent.  The 
cat,  however,  while  at  rest,  doubtless  knows  its  position  in  space  and  is  in- 
•tinctively  conscious  of  the  amount  of  movement  which  will  put  it  on  its  feet. 


304  SENSA  TIONS  OF  ORIENT  A  TION. 

doors,  and  never  bumped  against  closed  ones.  The 
visual  sense  had  here  been  rapidly  replaced  by  the 
tactual  and  auditive  senses.  And  it  appears  from 
Ewald's  investigations  that  even  after  the  labyrinths 
have  been  removed,  animals  gradually  learn  to  move 
about  again  quite  in  the  normal  fashion,  presumably 
because  the  eliminated  function  of  the  labyrinth  is 
now  performed  by  some  part  of  the  brain.  A  certain 
peculiar  weakness  of  the  muscles  alone  is  perceptible 
which  Ewald  ascribes  to  the  absence  of  the  stimulus 
which  is  otherwise  constantly  emitted  by  the  laby- 
rinth (the  labyrinth-tonus).  But  if  the  part  of  the 
brain  which  discharges  the  deputed  function  be  re- 
moved, the  animals  are  again  completely  disorien- 
tated and  absolutely  helpless. 

It  may  be  said  that  the  views  enunciated  by  Breuer, 
Crum  Brown  and  myself  in  1873  and  1874,  and  which 
are  substantially  a  fuller  and  richer  development  of 
Goltz's  idea,  have  upon  the  whole  been  substantiated. 
At  least  they  have  exercised  a  helpful  and  stimulative 
influence.  New  problems  have  of  course  arisen  in  the 
course  of  the  investigation  which  still  await  solution, 
and  much  work  remains  to  be  done.  At  the  same 
time  we  see  how  fruitful  the  renewed  co-operation  of 
the  various  special  departments  of  science  may  be- 
come after  a  period  of  isolation  and  invigorating  la- 
bor apart. 

I  may  be  permitted,  therefore,  to  consider  the  re- 
lation between  hearing  and  orientation  from  another 


SENSATIONS  OF  ORIENTATION.  303 

and  more  general  point  of  view.  What  we  call  the 
auditive  organ  is  in  the  lower  animals  simply  a  sac 
containing  auditive  stones.  As  we  ascend  the  scale, 
i,  2,  3  semi-circular  canals  gradually  develop  from 
them,  whilst  the  structure  of  the  otolith  organ  itself 
becomes  more  complicated.  Finally,  in  the  higher 
vertebrates,  and  particularly  in  the  mammals,  a  part 
of  the  latter  organ  (the  lagena)  becomes  the  cochlea, 
which  Helmholtz  explained  as  the  organ  for  sensa- 
tions of  tone.  In  the  belief  that  the  entire  labyrinth 
was  an  auditive  organ,  Helmholtz,  contrary  to  the  re- 
sults of  his  own  masterly  analysis,  originally  sought 
to  interpret  another  part  of  the  labyrinth  as  the  organ 
of  noises.  I  showed  a  long  time  ago  (1873)  that  every 
tonal  stimulus  by  shortening  the  duration  of  the  exci- 
tation to  a  few  vibrations,  gradually  loses  its  character 
of  pitch  and  takes  on  that  of  a  sharp,  dry  report  or 
noise.*  All  the  intervening  stages  between  tones  and 
noises  can  be  exhibited.  Such  being  the  case,  it  will 
hardly  be  assumed  that  one  organ  is  suddenly  and  at 
some  given  point  replaced  in  function  by  another.  On 
the  basis  of  different  experiments  and  reasonings  S. 
Exner  also  regards  the  assumption  of  a  special  organ 
for  the  sensing  of  noises  as  unnecessary. 

If  we  will  but  reflect  how  small  a  portion  of  the 
labyrinth  of  higher  animals  is  apparently  in  the  service 
of  the  sense  of  hearing,  and  how  large,  on  the  other 

*  See  the  Appendix  to  the  English  edition  of  my  Analysis  oftk*  Stnsations. 
Chicago,  1897. 


306  SENSATIONS  OF  ORIENTATION. 

hand,  the  portion  is  which  very  likely  serves  the  pur- 
poses of  orientation,  how  much  the  first  anatomical 
beginnings  of  the  auditive  sac  of  lower  animals  resem- 
ble that  part  of  the  fully  developed  labyrinth  which 
does  not  hear,  the  view  is  irresistibly  suggested  which 
Breuer  and  I  (1874,  1875)  expressed,  that  the  auditive 
organ  took  its  development  from  an  organ  for  sensing 
movements  by  adaptation  to  weak  periodic  motional 
stimuli,  and  that  many  apparatuses  in  the  lower  ani- 
mals which  are  held  to  be  organs  of  hearing  are  not 
auditive  organs  at  all.* 

This  view  appears  to  be  perceptibly  gaining 
ground.  Dr.  Kreidl  by  skilfully-planned  experiments 
has  arrived  at  the  conclusion  that  even  fishes  do  not 
hear,  whereas  E.  H.  Weber,  in  his  day,  regarded  the 
ossicles  which  unite  the  air-bladder  of  fishes  with  the 
labyrinth  as  organs  expressly  designed  for  conducting 
sound  from  the  former  to  the  latter,  f  Storensen  has 
investigated  the  excitation  of  sounds  by  the  air-blad- 
der of  fishes,  as  also  the  conduction  of  shocks  through 
Weber's  ossicles.  He  regards  the  air-bladder  as  par- 
ticularly adapted  for  receiving  the  noises  made  by 
other  fishes  and  conducting  them  to  the  labyrinth. 
He  has  heard  the  loud  grunting  tones  of  the  fishes 
in  South  American  rivers,  and  is  of  the  opinion  that 
they  allure  and  find  each  other  in  this  manner.  Ac- 
cording to  these  views  certain  fishes  are  neither  deaf 

*  Compare  my  Analysis  of  Sensations,  p.  133  ff, 

+  E.  H.  Weber,  De  aurt  tt  aitditu  hominis  tt  animalium,  LIpsiae,  i8ao. 


SENSATIONS  OF  ORIENTATION.  307 

nor  dumb.*  The  question  here  involved  might  be 
solved  perhaps  by  sharply  distinguishing  between  the 
sensation  of  hearing  proper,  and  the  perception  of 
shocks.  The  first-mentioned  sensation  may,  even  in 
the  case  of  many  vertebrates,  be  extremely  restricted, 
or  perhaps  even  absolutely  wanting.  But  besides  the 
auditive  function,  Weber's  ossicles  may  perfectly  well 
discharge  some  other  function.  Although,  as  Moreau 
has  shown,  the  air-bladder  itself  is  not  an  organ  of 
equilibrium  in  the  simple  physical  sense  of  Borelli, 
yet  doubtless  some  function  of  this  character  is  still 
reserved  for  it.  The  union  with  the  labyrinth  favors 
this  conception,  and  so  a  host  of  new  problems  rises 
here  before  us. 

I  should  like  to  close  with  a  reminiscence  from  the 
year  1863.  Helmholtz's  Sensations  of  Tone  had  just 
been  published  and  the  function  of  the  cochlea  now 
appeared  clear  to  the  whole  world.  In  a  private  con- 
versation which  I  had  with  a  physician,  the  latter  de- 
clared it  to  be  an  almost  hopeless  undertaking  to  seek 
to  fathom  the  function  of  the  other  parts  of  the  laby- 
rinth, whereas  I  in  youthful  boldness  maintained  that 
the  question  could  hardly  fail  to  be  solved,  and  that 
very  soon,  although  of  course  I  had  then  no  glimmer- 
ing of  how  it  was  to  be  done.  Ten  years  later  the 
question  was  substantially  solved. 

To-day,  after  having  tried  my  powers  frequently 
and  in  vain  on  many  questions,  I  no  longer  believe 

•  StOrensen,  Journ.  Anat.  Phys.,  London,  Vol.  39  (1895^ 


3o8  SENSATIONS  OF  ORIENTATION. 

that  we  can  make  short  work  of  the  problems  of  sci- 
ence. Nevertheless,  I  should  not  consider  an  "  ignor- 
abimus  "  as  an  expression  of  modesty,  but  rather  as 
the  opposite.  That  expression  is  a  suitable  one  only 
with  regard  to  problems  which  are  wrongly  formu- 
lated and  which  are  therefore  not  problems  at  all. 
Every  real  problem  can  and  will  be  solved  in  due 
course  of  time  without  supernatural  divination,  en- 
tirely by  accurate  observation  and  close,  searching 
thought. 


ON  SOME  PHENOMENA  ATTENDING 
THE  FLIGHT  OF  PROJECTILES.* 


M  I  have  led  my  ragamuffins  where  they  were 
peppered.'  '—Falstuff. 

"  He  goes  but  to  see  a  noise  that  he  heard." — 
Midsummer  Night's  Dream. 

nPO  SHOOT,  in  the  shortest  time  possible,  as  many 
-*-  holes  as  possible  in  one  another's  bodies,  and 
not  always  for  exactly  pardonable  objects  and  ideals, 
seems  to  have  risen  to  the  dignity  of  a  duty  with  mod- 
ern men,  who,  by  a  singular  inconsistency,  and  in 
subservience  to  a  diametrically  contrary  ideal,  are 
bound  by  the  equally  holy  obligation  of  making  these 
holes  as  small  as  possible,  and,  when  made,  of  stop- 
ping them  up  and  of  healing  them  as  speedily  as 
possible.  Since,  then,  shooting  and  all  that  appertains 
thereto,  is  a  very  important,  if  not  the  most  important, 
affair  of  modern  life,  you  will  doubtless  not  be  averse 
to  giving  your  attention  for  an  hour  to  some  experi- 
ments which  have  been  undertaken,  not  for  advancing 
the  ends  of  war,  but  for  promoting  the  ends  of  sci- 

*A  Lecture  delivered  on  Nov.  to,  1897. 


310  PHOTOGRAPHY  OF  PROJECTILES. 

ence,  and  which  throw  some  light  on  the  phenomena 
attending  the  flight  of  projectiles. 

Modern  science  strives  to  construct  its  picture  of 
the  world  not  from  speculations  but  so  far  as  possible 
from  facts.  It  verifies  its  constructs  by  recourse  to 
observation.  Every  newly  observed  fact  completes 
its  world-picture,  and  every  divergence  of  a  construct 
from  observation  points  to  some  imperfection,  to  some 
lacuna  in  it.  What  is  seen  is  put  to  the  test  of,  and 
supplemented  by,  what  is  thought,  which  is  again 
naught  but  the  result  of  things  previously  seen.  It 
is  always  peculiarly  fascinating,  therefore,  to  subject 
to  direct  verification  by  observation,  that  is,  to  render 
palpable  to  the  senses,  something  which  we  have  only 
theoretically  excogitated  or  theoretically  surmised. 

In  1 88 1,  on  hearing  in  Paris  the  lecture  of  the  Bel- 
gian artillerist  Melsens,  who  hazarded  the  conjecture 
that  projectiles  travelling  at  a  high  rate  of  speed  carry 
masses  of  compressed  air  before  them  which  are  in- 
strumental in  producing  in  bodies  struck  by  the  pro- 
jectiles certain  well-known  facts  of  the  nature  of  ex- 
plosions, the  desire  arose  in  me  of  experimentally  test- 
ing his  conjecture  and  of  rendering  the  phenomenon, 
if  it  really  existed,  perceptible.  The  desire  was  the 
stronger  as  I  could  say  that  all  the  means  for  realis- 
ing it  existed,  and  that  I  had  in  part  already  used  and 
tested  them  for  other  purposes. 

And  first  let  us  get  clear  regarding  the  difficulties 
which  have  to  be  surmounted.     Our  task  is  that  of 


PHOTOGRAPHY  OF  PROJECTILES.  311 

observing  a  bullet  or  other  projectile  which  is  rushing 
through  space  at  a  velocity  of  many  hundred  yards  a 
second,  together  with  the  disturbances  which  the  bul- 
let causes  in  the  surrounding  atmosphere.  Even  the 
opaque  solid  body  itself,  the  projectile,  is  only  excep- 
tionally visible  under  such  circumstances — only  when 
it  is  of  considerable  size  and  when  we  see  its  line  of 
flight  in  strong  perspective  abridgement  so  that  the 
velocity  is  apparently  diminished.  We  see  a  large 
projectile  quite  clearly  when  we  stand  behind  the  can- 
non and  look  steadily  along  its  line  of  flight  or  in  the 
less  pleasant  case  when  the  projectile  is  speeding  to- 
wards us.  There  is,  however,  a  very  simple  and  effec- 
tive method  of  observing  swiftly  moving  bodies  with  as 
little  trouble  as  if  they  were  held  at  rest  at  some  point 
in  their  path.  The  method  is  that  of  illumination  by 
a  brilliant  electric  spark  of  extremely  short  duration 
in  a  dark  room.  But  since,  for  the  full  intellectual 
comprehension  of  a  picture  presented  to  the  eye,  a 
certain,  not  inconsiderable  interval  of  time  is  neces 
sary,  the  method  of  instantaneous  photography  will 
naturally  also  be  employed.  The  pictures,  which  are 
of  extremely  minute  duration,  are  thus  permanently 
recorded  and  can  be  examined  and  analysed  at  one's 
convenience  and  leisure. 

With  the  difficulty  just  mentioned  is  associated 
still  another  and  greater  difficulty  which  is  due  to  the 
air.  The  atmosphere  in  its  usual  condition  is  gen- 
erally not  visible  even  when  at  rest.  But  the  task  pre- 


312  PHOTOGRAPHY  OF  PROJECTILES. 

sented  to  us  is  to  render  visible  masses  of  air  which 
in  addition  are  moving  with  a  high  velocity. 

To  be  visible,  a  body  must  either  emit  light  itself, 
must  shine,  or  must  affect  in  some  way  the  light  which 
falls  upon  it,  must  take  up  that  light  entirely  or  partly, 
absorb  it,  or  must  have  a  deflective  effect  upon  it,  that 
is,  reflect  or  refract  it.  We  cannot  see  the  air  as  we 
can  a  flame,  for  it  shines  only  exceptionally,  as  in  a 
Geissler's  tube.  The  atmosphere  is  extremely  trans- 
parent and  colorless ;  it  cannot  be  seen,  therefore,  as 
a  dark  or  colored  body  can,  or  as  chlorine  gas  can, 
or  vapor  of  bromine  or  iodine.  Air,  finally,  has  so 
small  an  index  of  refraction  and  so  small  a  deflective 
influence  upon  light,  that  the  refractive  effect  is  com- 
monly imperceptible  altogether. 

A  glass  rod  is  visible  in  air  or  in  water,  but  it  is 
almost  invisible  in  a  mixture  of  benzol  and  bisulphuret 
of  carbon,  which  has  the  same  mean  index  of  refrac- 
tion as  the  glass.  Powdered  glass  in  the  same  mix- 
ture has  a  vivid  coloring,  because  owing  to  the  de- 
composition of  the  colors  the  indices  are  the  same 
for  only  one  color  which  traverses  the  mixture  unim- 
peded, whilst  the  other  colors  undergo  repeated  re- 
flexions.* 

Water  is  invisible  in  water,  alcohol  in  alcohol.  But 
if  alcohol  be  mixed  with  water  the  flocculent  streaks 
of  the  alcohol  in  the  water  will  be  seen  at  once  and 


•Christiansen,  Wiedeman*'*  A**ate*,  XXIII.  S.  398,  XXIV.,  p.  439  (1884 

1885). 


PHOTOGRAPHY  OF  PROJECTILES.  313 

vice  versa.  And  in  like  manner  the  air,  too,  under 
favorable  circumstances,  may  be  seen.  Over  a  roof 
heated  by  the  burning  sun,  a  tremulous  wavering  of 
objects  is  noticeable,  as  there  is  also  over  red-hot 
stoves,  radiators,  and  registers.  In  all  these  cases 
tiny  flocculent  masses  of  hot  and  cold  air,  of  slightly 
differing  refrangibility,  are  mingled  together. 

In  like  manner  the  more  highly  refracting  parts  of 
non-homogeneous  masses  of  glass,  the  so-called  striae 
or  imperfections  of  the  glass,  are  readily  detectible 
among  the  less  refracting  parts  which  constitute  the 
bulk  of  the  same.  Such  glasses  are  unserviceable  for 
optical  purposes,  and  special  attention  has  been  de- 
voted to  the  investigation  of  the  methods  for  eliminat- 
ing or  avoiding  these  defects.  The  result  has  been 
the  development  of  an  extremely  delicate  method  for 
detecting  optical  faults — the  so-called  method  of  Fou- 
cault  and  Toepler — which  is  suitable  also  for  our 
present  purpose. 

Even  Huygens  when  trying  to  detect  the  presence 
of  striae  in  polished  glasses  viewed  them  under  oblique 
illumination,  usually  at  a  considerable  distance,  so  as 
to  give  full  scope  to  the  aberrations,  and  had  recourse 
for  greater  exactitude  to  a  telescope.  But  the  method 
was  carried  to  its  highest  pitch  of  perfection  in  1867 
by  Toepler  who  employed  the  following  procedure : 
A  small  luminous  source  a  (Fig.  49)  illuminates  a  lens 
L  which  throws  an  image  b  of  the  luminous  source. 
If  the  eye  be  so  placed  that  the  image  falls  on  the 


314  PHOTOGRAPHY  OF  PROJEC7ILES. 

pupil,  the  entire  lens,  if  perfect,  will  appear  equally 
illuminated,  for  the  reason  that  all  points  of  it  send 
out  rays  to  the  eye.  Coarse  imperfections  of  form  or 
of  homogeneity  are  rendered  visible  only  in  case  the 
aberrations  are  so  large  that  the  light  from  many  spots 
passes  by  the  pupil  of  the  eye.  But  if  the  image  b  be 
partly  intercepted  by  the  edge  of  a  small  slide,  then 
those  spots  in  the  lens  as  thus  partly  darkened  will 
appear  brighter  whose  light  by  its  greater  aberrations 
still  reaches  the  eye  in  spite  of  the  intercepting  slide, 
while  those  spots  will  appear  darker  which  in  conse- 


Fig.  49- 

quence  of  aberration  in  the  other  direction  throw  their 
light  entirely  upon  the  slide.  This  artifice  of  the  in- 
tercepting slide  which  had  previously  been  employed 
by  Foucault  for  the  investigation  of  the  optical  imper- 
fections of  mirrors  enhances  enormously  the  delicacy 
of  the  method,  which  is  still  further  augmented  by 
Toepler's  employment  of  a  telescope  behind  the  slide. 
Toepler's  method,  accordingly,  enjoys  all  the  advan- 
tages of  the  Huygens  and  the  Foucault  procedure 
combined.  It  is  so  delicate  that  the  minutest  irregu- 
larities in  the  air  surrounding  the  lens  can  be  rendered 
distinctly  visible,  as  I  shall  show  by  an  example.  I 


PHOTOGRAPHY  OF  PROJECTILES.  315 

place  a  candle  before  the  lens  L  (Fig.  50)  and  so  ar- 
range a  second  lens  M  that  the  flame  of  the  candle  is 
imaged  upon  the  screen  S.  As  soon  as  the  intercept- 
ing slide  is  pushed  into  the  focus,  b,  of  the  light  issu- 
ing from  a,  you  see  the  images  of  the  changes  of 
density  and  the  images  of  the  movements  induced  in 
the  air  by  the  flame  quite  distinctly  upon  the  screen. 
The  distinctness  of  the  phenomenon  as  a  whole  de- 
pends upon  the  position  of  the  intercepting  slide  b. 
The  removal  of  b  increases  the  illumination  but  de- 
creases the  distinctness.  If  the  luminous  source  a  be 

8 
L  M 


S  I 

Fig.  50. 

removed,  we  see  the  image  of  the  candle  flame  only 
upon  the  screen  S.  If  we  remove  the  flame  and  allow 
a  to  continue  shining,  the  screen  S  will  appear  uni- 
formly illuminated. 

After  Toepler  had  sought  long  and  in  vain  to  ren- 
der the  irregularities  produced  in  air  by  sound-waves 
visible  by  this  principle,  he  was  at  last  conducted  to 
his  goal  by  the  favorable  circumstances  attending  the 
production  of  electric  sparks.  The  waves  generated 
in  the  air  by  electric  sparks  and  accompanying  the 
explosive  snapping  of  the  same,  are  of  sufficiently 


3i6  PHOTOGRAPHY  OF  PROJECTILES. 

short  period  and  sufficiently  powerful  to  be  rendered 
visible  by  these  methods.  Thus  we  see  how  by  a 
careful  regard  for  the  merest  and  most  shadowy  indi- 
cations of  a  phenomenon  and  by  slight  progressive 
and  appropriate  alterations  of  the  circumstances  and 
the  methods,  ultimately  the  most  astounding  results 
can  be  attained.  Consider,  for  example,  two  such 
phenomena  as  the  rubbing  of  amber  and  the  electric 
lighting  of  modern  streets.  A  person  ignorant  of  the 
myriad  minute  links  that  join  these  two  things  to- 
gether, will  be  absolutely  nonplussed  at  their  connex- 
ion, and  will  comprehend  it  no  more  than  the  ordinary 
observer  who  is  unacquainted  with  embryology,  anat- 
omy, and  paleontology  will  understand  the  connexion 
between  a  saurian  and  a  bird.  The  high  value  and 
significance  of  the  co-operation  of  inquirers  through 
centuries,  where  each  has  but  to  take  up  the  thread  of 
work  of  his  predecessors  and  spin  it  onwards,  is  ren- 
dered forcibly  evident  by  such  examples.  And  such 
knowledge  destroys,  too,  in  the  clearest  manner  imag- 
inable that  impression  of  the  marvellous  which  the 
spectator  may  receive  from  science,  and  at  the  same 
time  is  a  most  salutary  admonishment  to  the  worker 
in  science  against  superciliousness.  I  have  also  to 
add  the  sobering  remark  that  all  our  art  would  be  in 
vain  did  not  nature  herself  afford  at  least  some  slight 
guiding  threads  leading  from  a  hidden  phenomenon 
into  the  domain  of  the  observable.  And  so  it  need 
not  surprise  us  that  once  under  particularly  favor- 


PHOTOGRAPHY  OF  PROJECTILES.  317 

able  circumstances  an  extremely  powerful  sound-wave 
which  had  been  caused  by  the  explosion  of  several 
hundred  pounds  of  dynamite  threw  a  directly  visible 
shadow  in  the  sunlight,  as  Boys  has  recently  told  us. 
If  the  sound-waves  were  absolutely  without  influence 
upon  the  light,  this  could  not  have  occurred,  and  all 
our  artifices  would  then,  too,  be  in  vain.  And  so, 
similarly,  the  phenomenon  accompanying  projectiles 
which  I  am  about  to  show  you  was  once  in  a  very  im- 
perfect manner  incidentally  seen  by  a  French  artiller- 
ist, Journ6e,  while  that  observer  was  simply  following 
the  line  of  flight  of  a  projectile  with  a  telescope,  just 
as  also  the  undulations  produced  by  candle  flames  are 
in  a  weak  degree  directly  visible  and  in  the  bright  sun- 
light are  imaged  in  shadowy  waves  upon  a  uniform 
white  background. 

Instantaneous  illumination  by  the  electric  spark, 
the  method  of  rendering  visible  small  optical  differ- 
ences or  striae,  which  may  hence  be  called  the  striate, 
or  differential,  method,*  invented  by  Foucault  and 

*The  German  phrase  is  Schlierenmethode,  by  which  term  the  method  is 
known  even  by  American  physicists.  It  is  also  called  in  English  the  "  shadow- 
method."  But  a  term  is  necessary  which  will  cover  all  the  derivatives,  and 
so  we  have  employed  alternatively  the  words  striate  and  differential.  The 
etymology  of  schlieren,  it  would  seem,  is  uncertain.  Its  present  use  is  derived 
from  its  technological  signification  in  glass-manufacturing,  where  by  die 
Scklieren  are  meant  the  wavy  streaks  and  imperfections  in  glass.  Hence  its 
application  to  the  method  for  detecting  small  optical  difference*  and  faults 
generally.  Professor  Crew  of  Evanston  suggests  to  the  translator  that  schlie- 
ren  may  be  related  to  our  slur  (L.  G.,sluren,  to  trail,  to  draggle),  a  conjecture 
which  is  doubtless  correct  and  agrees  both  with  the  meaning  of  tcklieren  as 
given  in  ths  large  German  dictionaries  and  with  the  intransitive  use  of  our 
own  verb  slur,  the  faults  in  question  being  conceived  as  "  trailings,"  "  streak- 
ings,"  etc,—  Trans. 


3i8  PHOTOGRAPHY  OF  PROJECTILES. 

Toepler,  and  finally  the  recording  of  the  image  by  a  pho- 
tographic plate, — these  therefore  are  the  chief  means 
which  are  to  lead  us  to  our  goal. 

I  instituted  my  first  experiments  in  the  summer  of 
1884  with  a  target-pistol,  shooting  the  bullet  through 
a  striate  field  as  described  above,  and  taking  care  that 
the  projectile  whilst  in  the  field  should  disengage  an 
illuminating  electric  spark  from  a  Leyden  jar  or  Frank- 
lin's pane,  which  spark  produced  a  photographic  im- 
pression of  the  projectile  upon  a  plate,  especially  ar- 
ranged for  the  purpose.  I  obtained  the  image  of  the 
projectile  at  once  and  without  difficulty.  I  also  readily 
obtained,  with  the  still  rather  defective  dry  plate  which 
I  was  using,  exceedingly  delicate  images  of  the  sound- 
waves (spark-waves).  But  no  atmospheric  condensa- 
tion produced  by  the  projectile  was  visible.  I  now 
determined  the  velocity  of  my  projectile  and  found  it 
to  be  only  240  metres  per  second,  or  considerably  less 
than  the  velocity  of  sound  (which  is  340  metres  per 
second).  I  saw  immediately  that  under  such  circum- 
stances no  noticeable  compression  of  the  air  could  be 
produced,  for  any  atmospheric  compression  must  of 
necessity  travel  forward  at  the  same  speed  with  sound 
(340  metres  per  second)  and  consequently  would  be 
always  ahead  of  and  speeding  away  from  the  projec- 
tile. 

I  was  so  thoroughly  convinced,  however,  of  the 
existence  of  the  supposed  phenomenon  at  a  velocity 
exceeding  340  metres  per  second,  that  I  requested 


PHOTOGRAPHY  OF  PROJECTILES.  319 

Professor  Salcher,  of  Fiume,  an  Austrian  port  on  the 
Gulf  of  Quarnero,  to  undertake  the  experiment  with 
projectiles  travelling  at  a  high  rate  of  speed.  In  the 
summer  of  1886  Salcher  in  conjunction  with  Professor 
Riegler  conducted  in  a  spacious  and  suitable  apart- 
ment placed  at  their  disposal  by  the  Directors  of  the 
Royal  Imperial  Naval  Academy,  experiments  of  the 
kind  indicated  and  conforming  in  method  exactly  to 
those  which  I  had  instituted,  with  the  precise  results 
expected.  The  phenomenon,  in  fact,  accorded  per- 
fectly with  the  a  priori  sketch  of  it  which  I  had  drafted 
previously  to  the  experiment.  As  the  experimenting 
was  continued,  new  and  unforeseen  features  made  their 
appearance. 

It  would  be  unfair,  of  course,  to  expect  from  the 
very  first  experiments  faultless  and  highly  distinct  pho- 
tographs. It  was  sufficient  that  success  was  secured 
and  that  I  had  convinced  myself  that  further  labor 
and  expenditure  would  not  be  vain.  And  on  this 
score  I  am  greatly  indebted  to  the  two  gentlemen 
above  mentioned. 

The  Austrian  Naval  Department  subsequently 
placed  a  cannon  at  Salcher's  disposal  in  Pola,  an 
Adriatic  seaport,  and  I  myself,  together  with  my  son, 
then  a  student  of  medicine,  having  received  and  ac- 
cepted a  courteous  invitation  from  Krupp,  repaired  to 
Meppen,  a  town  in  Hanover,  where  we  conducted 
with  only  the  necessary  apparatus  several  experiments 
on  the  open  artillery  range.  All  these  experiments 


32J  PHOTOGRAPHY  OF  PROJECTILES. 

furnished  tolerably  good  and  complete  pictures.  Some 
little  progress,  too,  was  .made.  The  outcome  of  our 
experience  on  both  artillery  ranges,  however,  was  the 
settled  conviction  that  really  good  results  could  be 
obtained  only  by  the  most  careful  conduct  of  the  ex- 
periments in  a  laboratory  especially  adapted  to  the 
purpose.  The  expensiveness  of  the  experiments  on 
a  large  scale  was  not  the  determining  consideration 
here,  for  the  size  of  the  projectile  is  indifferent.  Given 
the  same  velocity  and  the  results  are  quite  similar, 
whether  the  projectiles  are  large  or  small.  On  the 
other  hand,  in  a  laboratory  the  experimenter  has  per- 
fect control  over  the  initial  velocity,  which,  provided 
the  proper  equipment  is  at  hand,  can  be  altered  at 
will  simply  by  altering  the  charge  and  the  weight  of 
the  projectile.  The  requisite  experiments  were  ac- 
cordingly conducted  by  me  in  my  laboratory  at  Prague, 
partly  in  conjunction  with  my  son  and  partly  after- 
wards by  him  alone.  The  latter  are  the  most  per- 
fect and  I  shall  accordingly  speak  in  detail  here  of 
these  only. 

Picture  to  yourself  an  apparatus  for  detecting  op- 
tical striae  set  up  in  a  dark  room.  In  order  not  to 
make  the  description  too  complicated,  I  shall  give  the 
essential  features  only  of  the  apparatus,  leaving  out 
of  account  altogether  the  minuter  details  which  are 
rather  of  consequence  for  the  technical  performance 
of  the  experiment  than  for  its  understanding.  We 
suppose  the  projectile  speeding  on  its  path,  accord- 


PHOTOGRAPHY  OF  PROJECTILES. 


ingly,  through  the  field  of  our  differential  optical  ap- 
paratus. On  reaching  the  centre  of  the  field  (Fig.  51) 
the  projectile  disengages  an  illuminating  electric  spark 
a,  and  the  image  of  the  projectile,  so  produced,  is  pho- 
tographically impressed  upon  the  plate  of  the  cam- 
era behind  the  intercepting  slide  b.  In  the  last  and 
best  experiments  the  lens  L  was  replaced  by  a  spheri- 
cal silvered-glass  mirror  made  by  K.  Fritsch  (form- 
erly Prokesch)  of  Vienna,  whereby  the  apparatus  was 

L 


Fig.  51. 


naturally  more  complicated  than  it  appears  in  our  dia- 
gram. The  projectile  having  been  carefully  aimed 
passes  in  crossing  the  differential  field  between  two 
vertical  isolated  wires  which  are  connected  with  the 
two  coatings  of  a  Leyden  jar,  and  completely  filling 
the  space  between  the  wires  discharges  the  jar.  In 
the  axis  of  the  differential  apparatus  the  circuit  has  a 
second  gap  a  which  furnishes  the  illuminating  spark, 
the  image  of  which  falls  on  the  intercepting  slide  b. 
The  wires  in  the  differential  field  having  occasioned 


322  PHOTOGRAPHY  OF  PROJECTILES. 

manifold  disturbances  were  subsequently  done  away 
with.  In  the  new  arrangement  the  projectile  passes 
through  a  ring  (see  dotted  line,  Fig.  51),  to  the  air  in 
which  it  imparts  a  sharp  impulse  which  travels  for- 
ward in  the  tube  r  as  a  sound-wave  having  the  ap- 
proximate velocity  of  340  metres  per  second,  topples 
over  through  the  aperture  of  an  electric  screen  the 
flame  of  a  candle  situated  at  the  other  opening  of  the 
tube,  and  so  discharges  the  jar.  The  length  of  the 
tube  r  is  so  adjusted  that  the  discharge  occurs  the 
moment  the  projectile  enters  the  centre  of  the  now 
fully  clear  and  free  field  of  vision.  We  will  also  leave 
out  of  account  the  fact  that  to  secure  fully  the  suc- 
cess of  the  experiment,  a  large  jar  is  first  discharged 
by  the  flame,  and  that  by  the  agency  of  this  first  dis- 
charge the  discharge  of  a  second  small  jar  having  a 
spark  of  very  short  period  which  furnishes  the  spark 
really  illuminating  the  projectile  is  effected.  Sparks 
from  large  jars  have  an  appreciable  duration,  and 
owing  to  the  great  velocity  of  the  projectiles  furnish 
blurred  photographs  only.  By  carefully  husbanding 
the  light  of  the  differential  apparatus,  and  owing  to 
the  fact  that  much  more  light  reaches  the  photo- 
graphic plate  in  this  way  than  would  otherwise  reach 
it,  we  can  obtain  beautiful,  strong,  and  sharp  photo- 
graphs with  incredibly  small  sparks.  The  contours  of 
the  pictures  appear  as  very  delicate  and  very  sharp, 
closely  adjacent  double  lines.  From  their  distance 
from  one  another,  and  from  the  velocity  of  the  projec- 


PHOTOGRAPHY  OF  PROJECTILES.  323 

tile,  the  duration  of  the  illumination,  or  of  the  spark, 
is  found  to  be  ¥Tr?7V?n7  °*  a  second.  It  is  evident, 
therefore,  that  experiments  with  mechanical  snap 
slides  can  furnish  no  results  worthy  of  the  name. 

Let  us  consider  now  first  the  picture  of  a  projec- 
tile in  the  rough,  as  represented  in  Figure  52,  and 
then  let  us  examine  it  in  its  photographic  form  as  seen 


Fig.  52- 

in  Figure  53.  The  latter  picture  is  of  a  shot  from  an 
Austrian  Mannlicher  rifle.  If  I  were  not  to  tell  you 
what  the  picture  represented  you  would  very  likely 
imagine  it  to  be  a  bird's  eye  view  of  a  boat  b  moving 
swiftly  through  the  water.  In  front  you  see  the  bow- 
wave  and  behind  the  body  a  phenomenon  k  which 
closely  resembles  the  eddies  formed  in  the  wake  of  a 


324  PHOTOGRAPHY  OF  PROJECTILES. 

ship.  And  as  a  matter  of  fact  the  dark  hyperboloid 
arc  which  streams  from  the  tip  of  the  projectile  really 
is  a  compressed  wave  of  air  exactly  analogous  to  the 
bow-wave  produced  by  a  ship  moving  through  the 
water,  with  the  exception  that  the  wave  of  air  is  not 
a  surface-wave.  The  air-wave  is  produced  in  atmos- 


Fig.  53.    Photograph  of  a  blunted  projectile. 

pheric  space  and  encompasses  the  projectile  in  the 
form  of  a  shell  on  all  sides.  The  wave  is  visible  for 
the  same  reason  that  the  heated  shell  of  air  surround- 
ing the  candle  flame  of  our  former  experiments  is  vis- 
ible. And  the  cylinder  of  friction-heated  air  which  the 
projectile  throws  off  in  the  form  of  vortex  rings  really 
does  answer  to  the  water  in  the  wake  of  a  vessel. 


PHOTOGRAPHY  OF  PROJECTILES.  325 

Now  just  as  a  slowly  moving  boat  produces  no 
bow-wave,  but  the  bow-wave  is  seen  only  when  the 
boat  moves  with  a  speed  which  is  greater  than  the 
velocity  of  propagation  of  surface-waves  in  water,  so, 
in  like  manner,  no  wave  of  compression  is  visible  in 
front  of  a  projectile  so  long  as  the  speed  of  the  pro- 
jectile is  less  than  the  velocity  of  sound.  But  if  the 
speed  of  the  projectile  reaches  and  exceeds  the  velo- 
city of  sound,  then  the  head-wave,  as  we  shall  call  it, 
augments  noticeably  in  power,  and  is  more  and  more 
extended,  that  is,  the  angle  made  by  the  contours  of 
the  wave  with  the  direction  of  flight  is  more  and  more 
diminished,  just  as  when  the  speed  of  a  boat  is  in- 
creased a  similar  phenomenon  is  noticed  in  connexion 
with  the  bow-wave.  In  fact,  we  can  from  an  instan- 
taneous photograph  so  taken  approximately  estimate 
the  speed  with  which  the  projectile  is  travelling. 

The  explanation  of  the  bow-wave  of  a  ship  and 
that  of  the  head-wave  of  a  body  travelling  in  atmos- 
pheric space  both  repose  upon  the  same  principle, 
long  ago  employed  by  Huygens.  Conceive  a  number 
of  pebbles  to  be  cast  into  a  pond  of  water  at  regular 
intervals  in  such  wise  that  all  the  spots  struck  are  sit- 
uate in  the  same  straight  line,  and  that  every  spot 
subsequently  struck  lies  a  short  space  farther  to  the 
right.  The  spots  first  struck  will  furnish  then  the 
wave-circles  which  are  widest,  and  all  of  them  to- 
gether will,  at  the  points  where  they  are  thickest, 
form  a  sort  of  cornucopia  closely  resembling  the  bow- 


326  PHOTOGRAPHY  OF  PROJECTILES. 

wave.  (Fig.  54.)  The  resemblance  is  greater  the 
smaller  the  pebbles  are,  and  the  more  quickly  they 
succeed  each  other.  If  a  rod  be  dipped  into  the  water 
and  quickly  carried  along  its  surface,  the  falling  of 
the  pebbles  will  then  take  place,  so  to  speak,  uninter- 
ruptedly, and  we  shall  have  a  real  bow-wave.  If  we 
put  the  compressed  air-wave  in  the  place  of  the  sur- 
face-waves of  the  water,  we  shall  have  the  head-wave 
of  the  projectile. 


Fig.  54- 

You  may  be  disposed  to  say  now,  it  is  all  very 
pretty  and  interesting  to  observe  a  projectile  in  its 
flight,  but  of  what  practical  use  is  it  ? 

It  is  true,  I  reply,  one  cannot  wage  war  with  pho- 
tographed projectiles.  And  I  have  likewise  often  had 
to  say  to  medical  students  attending  my  lectures  on 
physics,  when  they  inquired  for  the  practical  value  of 
some  physical  observation,  "You  cannot,  gentlemen, 
cure  diseases  with  it."  I  had  also  once  to  give  my 
opinion  regarding  how  much  physics  should  be  taught 
at  a  school  for  millers,  supposing  the  instruction 
there  to  be  confined  exactly  to  what  was  necessary  for 


PHOTOGRAPHY  OF  PROJECTILES.  32; 

a  miller.  I  was  obliged  to  reply:  "A  miller  always 
needs  exactly  as  much  physics  as  he  knows."  Knowl- 
edge which  one  does  not  possess  one  cannot  use. 

Let  us  forego  entirely  the  consideration  that  as  a 
general  thing  every  scientific  advance,  every  new 
problem  elucidated,  every  extension  or  enrichment  of 
our  knowledge  of  facts,  affords  a  better  foundation  for 
practical  pursuits.  Let  us  rather  put  the  special 
question,  Is  it  not  possible  to  derive  some  really  prac- 
tical knowledge  from  our  theoretical  acquaintance 
with  the  phenomena  which  take  place  in  the  space 
surrounding  a  projectile? 

No  physicist  who  has  ever  studied  waves  of  sound 
or  photographed  them  will  have  the  least  doubt  re- 
garding the  sound-wave  character  of  the  atmospheric 
condensation  encompassing  the  head  of  a  flying  pro- 
jectile. We  have  therefore,  without  ado,  called  this 
condensation  the  head-wave. 

Knowing  this,  it  follows  that  the  view  of  Melsens 
according  to  which  the  projectile  carries  along  with 
it  masses  of  air  which  it  forces  into  the  bodies  struck, 
is  untenable.  A  forward-moving  sound-wave  is  not  a 
forward-moving  mass  of  matter  but  a  forward-moving 
form  of  motion,  just  as  a  water-wave  or  the  waves  of 
a  field  of  wheat  are  only  forward-moving  forms  of  mo- 
tion and  not  movements  of  masses  of  water  or  masses 
of  wheat. 

By  interference-experiments,  on  which  I  cannot 
touch  here  but  which  will  be  found  roughly  repre- 


328 


PHOTOGRAPHY  OF  PROJECTILES. 


sented  in  Figure  55,  it  was  found  that  the  bell-shaped 
head-wave  in  question  is  an  extremely  thin  shell  and 
that  the  condensations  of  the  same  are  quite  moder- 
ate, scarcely  exceeding  two-tenths  of  an  atmosphere. 
There  can  be  no  question,  therefore,  of  explosive  ef- 
fects in  the  body  struck  by  the  projectile  through  so 
slight  a  degree  of  atmospheric  compression.  The 
phenomena  attending  wounds  from  rifle  balls,  for  ex- 


ample,  are  not  to  be  explained  as  Melsens  and  Busch 
explain  them,  but  are  due,  as  Kocher  and  Reger  main- 
tain, to  the  effects  of  the  impact  of  the  projectile  it- 
self. 

A  simple  experiment  will  show  how  insignificant  is 
the  part  played  by  the  friction  of  the  air,  or  the  sup- 
posed conveyance  of  the  air  along  with  the  moving 
projectile.  If  the  photograph  of  the  projectile  be 


PHOTOGRAPHY  OF  PROJECTILES.  379 

taken  while  passing  through  a  flame,  i.  e.,  a  visible 
gas,  the  flame  will  be  seen  to  be,  not  torn  and  de- 
formed, but  smoothly  and  cleanly  perforated,  like  any 
solid  body.  Within  and  around  the  flame  the  con- 
tours of  the  head-wave  will  be  seen.  The  flickering, 
the  extinction  of  the  flame,  etc.,  take  place  only  after 
the  projectile  has  travelled  on  a  considerable  distance 
in  its  path,  and  is  then  affected  by  the  powder  gases 
which  hurry  after  the  bullet  or  by  the  air  preceding 
the  powder-gases. 

The  physicist  who  examines  the  head-wave  and 
recognises  its  sound-wave  character  also  sees  that  the 
wave  in  question  is  of  the  same  kind  with  the  short 
sharp  waves  produced  by  electric  sparks,  that  it  is  a 
«0/jr-wave.  Hence,  whenever  any  portion  of  the  head- 
wave  strikes  the  ear  it  will  be  heard  as  a  report.  Ap- 
pearances point  to  the  conclusion  that  the  projectile 
carries  this  report  along  with  it.  In  addition  to  this 
report,  which  advances  with  the  velocity  of  the  projec- 
tile and  so  usually  travels  at  a  speed  greater  than  the 
velocity  of  sound,  there  is  also  to  be  heard  the  report 
of  the  exploding  powder  which  travels  forward  with 
the  ordinary  velocity  of  sound.  Hence  two  explo- 
sions will  be  heard,  each  distinct  in  time.  The  cir- 
cumstance that  this  fact  was  long  misconstrued  by 
practical  observers  but  when  actually  noticed  fre- 
quently received  grotesque  explanations  and  that  ulti- 
mately my  view  was  accepted  as  the  correct  one,  ap- 
pears to  me  in  itself  a  sufficient  justification  that 


330  PHOTOGRAPHY  OF  PROJECTILES. 

researches  such  as  we  are  here  speaking  of  are  not  ut- 
terly superfluous  even  in  practical  directions.  That 
the  flashes  and  sounds  of  discharging  artillery  are 

used  for  estimating  the  distances  of  batteries  is  well 

o  ^ 

known,  and  it  stands  to  reason  that  any  unclear  the- 
oretical conception  of  the  facts  here  involved  will  se- 
riously affect  the  correctness  of  practical  calculations. 
It  may  appear  astonishing  to  a  person  hearing  it 
for  the  first  time,  that  a  single  shot  has  a  double  re- 
port due  to  two  different  velocities  of  propagation. 
But  the  reflexion  that  projectiles  whose  velocity  is  less 
than  the  velocity  of  sound  produce  no  head-waves  (be- 
cause every  impulse  imparted  to  the  air  travels  for- 
ward, that  is,  ahead,  with  exactly  the  velocity  of 
sound),  throws  full  light  when  logically  developed 
upon  the  peculiar  circumstance  above  mentioned.  If 
the  projectile  moves  faster  than  sound,  the  air  ahead 
of  it  cannot  recede  from  it  quickly  enough.  The  air 
is  condensed  and  warmed,  and  thereupon,  as  all  know, 
the  velocity  of  sound  is  augmented  until  the  head-wave 
travels  forward  as  rapidly  as  the  projectile  itself,  so 
that  there  is  no  need  whatever  of  any  additional  aug- 
mentation of  the  velocity  of  propagation.  If  such  a 
wave  were  left  entirely  to  itself,  it  would  increase  in 
length  and  soon  pass  into  an  ordinary  sound-wave, 
travelling  with  less  velocity.  But  the  projectile  is  al- 
ways behind  it  and  so  maintains  it  at  its  proper  den- 
sity and  velocity.  Even  if  the  projectile  penetrates  a 
piece  of  cardboard  or  a  board  of  wood,  which  patches 


PHOTOGRAPHY  OF  PROJECTILES.  331 

and  obstructs  the  head-wave,  there  will,  as  Figure  56 
shows,  immediately  appear  at  the  emerging  apex  a 
newly  formed,  not  to  say  newly  born,  head-wave.  We 
may  observe  on  the  cardboard  the  reflexion  and  dif- 
fraction of  the  head-wave,  and  by  means  of  a  flame 
its  refraction,  so  that  no  doubt  as  to  its  nature  can  re- 
main. 


Fig.  56. 

Permit  me,  now,  to  illustrate  the  most  essential  of 
the  points  that  I  have  just  adduced,  by  means  of  a  few 
rough  drawings  taken  from  older  and  less  perfect  pho- 
tographs. 

In  the  sketch  of  Figure  57  you  see  the  projectile, 
which  has  just  left  the  barrel  of  the  rifle,  touch  a  wire 
and  disengage  the  illuminating  spark.  At  the  apex  of 


332 


PHOTOGRAPHY  OF  PROJECTILES, 


the  projectile  you  already  see  the  beginnings  of  a 
powerful  head-wave,  and  in  front  of  the  wave  a  trans- 
parent fungiform  cluster.  This  latter  is  the  air  which 
has  been  forced  out  of  the  barrel  by  the  projectile. 
Circular  sound-waves,  noise-waves,  which  are  soon 
overtaken  by  the  projectile,  also  issue  from  the  barrel. 
But  behind  the  projectile  opaque  puffs  of  powder-gas 
rush  forth.  It  is  scarcely  necessary  to  add  that  many 


\ 


Fig.  57- 

other  questions  in  ballistics  may  be  studied  by  this 
method,  as,  for  example,  the  movement  of  the  gun- 
carriage. 

A  distinguished  French  artillerist,  M.  Gossot,  has 
applied  the  views  of  the  head-wave  here  given  in  quite 
a  different  manner.  The  practice  in  measuring  the 
velocity  of  projectiles  is  to  cause  the  projectile  to  pass 
through  wire  screens  placed  at  different  points  in  its 
path,  and  by  the  tearing  of  these  screens  to  give  rise 


PHO  /  OGKAPHY  OF  PROJECTILES.  333 

to  electro-magnetic  time-signals  on  falling  slabs  or 
rotating  drums.  Gossot  caused  these  signals  to  be 
made  directly  by  the  impact  of  the  head-wave,  did 
away  thus  with  the  wire  screens,  and  carried  the 
method  so  far  as  to  be  able  to  measure  the  velocities 
of  projectiles  travelling  in  high  altitudes,  where  the 
use  of  wire  screens  was  quite  out  of  the  question. 

The  laws  of  the  resistance  of  fluids  and  of  air  to 
bodies  travelling  in  them  form  an  extremely  compli- 
cated problem,  which  can  be  reasoned  out  very  sim- 
ply and  prettily  as  a  matter  of  pure  philosophy  but 
in  practice  offers  not  a  few  difficulties.  The  same 
body  having  the  velocity  2,  3,  4 ....  displaces  in  the 
same  interval  2,  3,  4  ...  times  the  same  mass  of  air, 
or  the  same  mass  of  fluid,  and  imparts  to  it  in  addition 
2,  3,  4,  ....  times  the  same  velocity.  But  for  this, 
plainly,  4,  9,  16  ....  times  the  original  force  is  re- 
quired. Hence,  the  resistance,  it  is  said,  increases 
with  the  square  of  the  velocity.  This  is  all  very  pretty 
and  simple  and  obvious.  But  practice  and  theory  are 
at  daggers'  points  here.  Practice  tells  us  that  when 
we  increase  the  velocity,  the  law  of  the  resistance 
changes.  For  every  portion  of  the  velocity  the  law  is 
different. 

The  studies  of  the  talented  English  naval  archi- 
tect, Froude,  have  thrown  light  upon  this  question. 
Froude  has  shown  that  the  resistance  is  conditioned 
by  a  combination  of  the  most  multifarious  phenom- 
ena. A  ship  in  motion  is  subjected  to  the  friction  of 


334  PHOTOGRAPHY  OF  PROJECTILES. 

the  water.  It  causes  eddies  and  it  generates  in  addi- 
tion waves  which  radiate  outward  from  it.  Every  one 
of  these  phenomena  are  dependent  upon  the  velocity 
in  some  different  manner,  and  it  is  consequently  not 
astonishing  that  the  law  of  the  resistance  should  be  a 
complicated  one. 

The  preceding  observations  suggest  quite  analog- 
ous reflexions  for  projectiles.  Here  also  we  have  fric- 
tion, the  formation  of  eddies,  and  the  generation  of 
waves.  Here,  also,  therefore,  we  should  not  be  sur- 
prised at  finding  the  law  of  the  resistance  of  the  air  a 
complicated  one,  nor  puzzled  at  learning  that  in  actu- 
ality the  law  of  resistance  changes  as  soon  as  the 
speed  of  the  projectile  exceeds  the  velocity  of  sound, 
for  this  is  the  precise  point  at  which  one  important 
element  of  the  resistance,  namely,  the  fownation  of 
waves,  first  comes  into  play. 

No  one  doubts  that  a  pointed  bullet  pierces  the 
air  with  less  resistance  than  a  blunt  bullet.  The 
photographs  themselves  show  that  the  head-wave  is 
weaker  for  a  pointed  projectile.  It  is  not  impossible, 
similarly,  that  forms  of  bullets  will  be  invented  which 
generate  fewer  eddies,  etc.,  and  that  we  shall  study 
these  phenomena  also  by  photography.  I  am  of  opin- 
ion from  the  few  experiments  which  I  have  made  in 
this  direction  that  not  much  more  can  be  done  by 
changing  the  form  of  the  projectile  when  the  velocity 
is  very  great,  but  I  have  not  gone  into  the  question 
thoroughly.  Researches  of  the  kind  we  are  consider- 


PHOTOGRAPHY  OF  PROJECTILES.  335 

ing  can  certainly  not  be  detrimental  to  practical  artil- 
lery, and  it  is  no  less  certain  that  experiments  by  ar- 
tillerists on  a  large  scale  will  be  of  undoubted  benefit 
to  physics. 

No  one  who  has  had  the  opportunity  of  studying 
modern  guns  and  projectiles  in  their  marvellous  per- 
fection, their  power  and  precision,  can  help  confessing 
that  a  high  technical  and  scientific  achievement  has 
found  its  incarnation  in  these  objects.  We  may  sur- 
render ourselves  so  completely  to  this  impression  as 
to  forget  for  a  moment  the  terrible  purposes  they 
serve. 

Permit  me,  therefore,  before  we  separate,  to  say  a 
few  words  on  this  glaring  contrast.  The  greatest  man 
of  war  and  of  silence  which  the  present  age  has  pro- 
duced once  asserted  that  perpetual  peace  is  a  dream, 
and  not  a  beautiful  dream  at  that.  We  may  accord 
to  this  profound  student  of  mankind  a  judgment  in 
these  matters  and  can  also  appreciate  the  soldier's 
horror  of  stagnation  from  all  too  lengthy  peace.  But 
it  requires  a  strong  belief  in  the  insuperableness  of 
medieval  barbarism  to  hope  for  and  to  expect  no 
great  improvement  in  international  relations.  Think 
of  our  forefathers  and  of  the  times  when  club  law 
ruled  supreme,  when  within  the  same  country  and  the 
same  state  brutal  assaults  and  equally  brutal  self- 
defence  were  universal  and  self-evident.  This  state 
of  affairs  grew  so  oppressive  that  finally  a  thousand 
and  one  circumstances  compelled  people  to  put  an 


336  PHOTOGRAPHY  OF  PROJECTILES. 

end  to  it,  and  the  cannon  had  most  to  say  in  accom- 
plishing the  work.  Yet  the  rule  of  club  law  was  not 
abolished  so  quickly  after  all.  It  had  simply  passed 
to  other  clubs.  We  must  not  abandon  ourselves  to 
dreams  of  the  Rousseau  type.  Questions  of  law  will 
in  a  sense  forever  remain  questions  of  might.  Even 
in  the  United  States  where  every  one  is  as  a  matter 
of  principle  entitled  to  the  same  privileges,  the  ballot 
according  to  Stallo's  pertinent  remark  is  but  a  milder 
substitute  for  the  club.  Nor  need  I  tell  you  that 
many  of  our  own  fellow-citizens  are  still  enamored  of 
the  old  original  methods.  Very,  very  gradually,  how- 
ever, as  civilisation  progresses,  the  intercourse  of  men 
tr^kes  on  gentler  forms,  and  no  one  who  really  knows 
the  good  old  times  will  ever  honestly  wish  them  back 
again,  however  beautifully  they  may  be  painted  and 
rhymed  about. 

In  the  intercourse  of  the  nations,  however,  the  old 
club  law  still  reigns  supreme.  But  since  its  rule  is 
taxing  the  intellectual,  the  moral,  and  the  material  re- 
sources of  the  nations  to  the  utmost  and  constitutes 
scarcely  less  a  burden  in  peace  than  in  war,  scarcely 
less  a  yoke  for  the  victor  than  for  the  vanquished,  it 
must  necessarily  grow  more  and  more  unendurable. 
Reason,  fortunately,  is  no  longer  the  exclusive  pos- 
session of  those  who  modestly  call  themselves  the 
upper  ten  thousand.  Here,  as  everywhere,  the  evil 
itself  will  awaken  the  intellectual  and  ethical  forces 
which  are  destined  to  mitigate  it.  Let  the  hate  of 


PHOTOGRAPHY  OF  PROJECTILES.  337 

races  and  of  nationalities  run  riot  as  it  may,  the  inter- 
course of  nations  will  still  increase  and  grow  more  in- 
timate. By  the  side  of  the  problems  which  separate 
nations,  the  great  and  common  ideals  which  claim  the 
exclusive  powers  of  the  men  of  the  future  appear  one 
after  another  in  greater  distinctness  and  in  greater 
might. 


ON  INSTRUCTION   IN  THE  CLASSICS 
AND  THE  SCIENCES.* 


"PERHAPS  the  most  fantastic  proposition  that  Mau- 
-*-•  perttris,f  the  renowned  president  of  the  Berlin 
Academy,  ever  put  forward  for  the  approval  of  his 

*An  address  delivered  before  the  Congress  of  Delegates  of  the  German 
Realschulmannerverein,  at  Dortmund,  April  16,  1886.  The  full  title  of  the 
address  reads  •  "  On  the  Relative  Educational  Value  of  the  Classics  and  the 
Mathematico-Physical  Sciences  in  Colleges  and  High  Schools." 

Although  substantially  contained  in  an  address  which  I  was  to  have  made 
at  the  meeting  of  Natural  Scientists  at  Salzburg  in  1881  (deferred  on  account 
of  the  Paris  Exposition),  and  in  the  Introduction  to  a  course  of  lectures  on 
"Physical  Instruction  in  Preparatory  Schools,"  which  I  delivered  in  1883,  the 
invitation  of  the  German  Realschulmannerverein  afforded  me  the  first  oppor- 
tunity of  putting  my  views  upon  this  subject  before  a  large  circle  of  readers. 
Owing  to  the  place  and  circumstances  of  delivery,  my  remarks  apply  of  course, 
primarily,  only  to  German  schools,  but,  with  slight  modifications,  made  in 
this  translation,  are  not  without  force  for  the  institutions  of  other  countries. 
In  giving  here  expression  to  a  strong  personal  conviction  formed  long  ago,  it 
is  a  matter  of  deep  satisfaction  to  me  to  find  that  they  agree  in  many  points 
with  the  views  recently  advanced  in  independent  form  by  Paulsen  (Geschichte 
des  gelehrten  Unterrichts,  Leipsic,  1885)  and  Frary  (La  question  du  latin, 
Paris,  Cerf,  1885).  It  is  not  my  desire  nor  effort  here  to  say  much  that  is  new, 
but  merely  to  contribute  iny  mite  towards  bringing  about  the  inevitable  revo- 
lution now  preparing  in  the  world  of  elementary  instructicn.  In  the  opinion 
of  experienced  educationists  the  first  result  of  that  revolution  will  be  to  make 
Greek  and  mathematics  alternately  optional  subjects  in  the  higher  classes  of 
the  German  Gymnasium  and  in  the  corresponding  institutions  of  other  coun- 
tries, as  has  been  done  in  the  splendid  system  of  instruction  in  Denmark.  The 
gap  between  the  German  classical  Gymnasium  and  the  German  Realgymna- 
sium.  or  between  classical  and  scientific  schools  generally,  can  thus  be  bridged 
over,  and  the  remaining  inevitable  transformations  will  then  be  accomplished 
in  relative  peace  and  quiet.  (Prague,  May,  1886.) 

t  Maupertuis,  CEwres,  Dresden,  1752,  p.  339. 


ON  THE  CLASSICS  AND  THE  SCIENCES.        339 

contemporaries  was  that  of  founding  a  city  in  which, 
to  instruct  and  discipline  young  students,  only  Latin 
should  be  spoken.  Maupertuis's  Latin  city  remained 
an  idle  wish.  But  for  centuries  Latin  and  Greek  in- 
stitutions exist  in  which  our  children  spend  a  goodly 
portion  of  their  days,  and  whose  atmosphere  constantly 
surrounds  them,  even  when  without  their  walls. 

For  centuries  instruction  in  the  ancient  languages 
has  been  zealously  cultivated.  For  centuries  its  neces- 
sity has  been  alternately  championed  and  contested. 
More  strongly  than  ever  are  authoritative  voices  now 
raised  against  the  preponderance  of  instruction  in  the 
classics  and  in  favor  of  an  education  more  suited  to 
the  needs  of  the  time,  especially  for  a  more  generous 
treatment  of  mathematics  and  the  natural  sciences. 

In  accepting  your  invitation  to  speak  here  on  the 
relative  educational  value  of  the  classical  and  the 
mathematico-physical  sciences  in  colleges  and  high 
schools,  I  find  my  justification  in  the  duty  and  the 
necessity  laid  upon  every  teacher  of  forming  from  his 
own  experiences  an  opinion  upon  this  important  ques- 
tion, as  partly  also  in  the  special  circumstance  that  in 
my  youth  I  was  personally  under  the  influence  of 
school-life  for  only  a  short  time,  just  previous  to  my 
entering  the  university,  and  had,  therefore,  ample  op- 
portunity to  observe  the  effects  of  widely  different 
methods  upon  my  own  person. 

Passing,  now,  to  a  review  of  the  arguments  which 
the  advocates  of  instruction  in  the  classics  advance, 


340         ON  THE  CLASSICS  AND  THE  SCIENCES. 

and  of  what  the  adherents  of  instruction  in  the  physi- 
cal sciences  in  their  turn  adduce,  we  find  ourselves  in 
rather  a  perplexing  position  with  respect  to  the  argu- 
ments of  the  first  named.  For  these  have  been  differ- 
ent at  different  times,  and  they  are  even  now  of  a  very 
multifarious  character,  as  must  be  where  men  advance, 
in  favor  of  an  institution  that  exists  and  which  they  are 
determined  to  retain  at  any  cost,  everything  they  can 
possibly  think  of.  We  shall  find  here  much  that  has 
evidently  been  brought  forward  only  to  impress  the 
minds  of  the  ignorant;  much,  too,  that  was  advanced 
in  good  faith  and  which  is  not  wholly  without  founda- 
tion. We  shall  get  a  fair  idea  of  the  reasoning  employed 
by  considering,  first,  the  arguments  that  have  grown 
out  of  the  historical  circumstances  connected  with  the 
original  introduction  of  the  classics,  and,  lastly,  those 
which  were  subsequently  adduced  as  accidental  after- 
thoughts. 

* 
*  * 

Instruction  in  Latin,  as  Paulsen*  has  minutely 
shown,  was  introduced  by  the  Roman  Church  along 
with  Christianity.  With  the  Latin  language  were  also 
transmitted  the  scant  and  meagre  remnants  of  ancient 
science.  Whoever  wished  to  acquire  this  ancient  edu- 
cation, then  the  only  one  worthy  of  the  name,  for  him 
the  Latin  language  was  the  only  and  indispensable 
means;  such  a  person  had  to  learn  Latin  to  rank 
among  educated  people. 

*F.  Paulsen,  Geschichte  des  gelehrttn  Unterrtchts,  Leipslc,  1885. 


ON  THE  CLASSICS  AND  THE  SCIENCES.        341 

The  wide-spread  influence  of  the  Roman  Church 
wrought  many  and  various  results.  Among  those  for 
which  all  are  glad,  we  may  safely  count  the  establish- 
ment of  a  sort  of  uniformity  among  the  nations  and  of  a 
regular  international  intercourse  by  means  of  the  Latin 
language,  which  did  much  to  unite  the  nations  in  the 
common  work  of  civilisation,  carried  on  from  the  fif- 
teenth to  the  eighteenth  century.  The  Latin  language 
was  thus  long  the  language  of  scholars,  and  instruc- 
tion in  Latin  the  road  to  a  liberal  education — a  shib- 
boleth still  employed,  though  long  inappropriate. 

For  scholars  as  a  class,  it  is  to  be  regretted,  per- 
haps, that  Latin  has  ceased  to  be  the  medium  of  inter- 
national communication.  But  the  attributing  of  the 
loss  of  this  function  by  the  Latin  language  to  its  inca- 
pacity to  accommodate  itself  to  the  numerous  new 
ideas  and  conceptions  which  have  arisen  in  the  course 
of  the  development  of  science  is,  in  my  opinion,  wholly 
erroneous.  It  would  be  difficult  to  find  a  modern 
scientist  who  had  enriched  science  with  as  many  new 
ideas  as  Newton  has,  yet  Newton  knew  how  to  ex- 
press those  ideas  very  correctly  and  precisely  in  the 
Latin  language.  If  this  view  were  correct,  it  would 
also  hold  true  of  every  living  language.  Originally 
every  language  has  to  adapt  itself  to  new  ideas. 

It  is  far  more  likely  that  Latin  was  displaced  as 
the  literary  vehicle  of  science  by  the  influence  of  the 
nobility.  By  their  desire  to  enjoy  the  fruits  of  litera- 
ture and  science,  through  a  less  irksome  medium  than 


342         ON  THE  CLASSICS  AND  THE  SCIENCES. 

Latin,  the  nobility  performed  for  the  people  at  large 
an  undeniable  service.  For  the  days  were  now  past 
when  acquaintance  with  the  language  and  literature  of 
science  was  restricted  to  a  caste,  and  in  this  step,  per- 
haps, was  made  the  most  important  advance  of  modern 
times.  To-day,  when  international  intercourse  is  firmly 
established  in  spite  of  the  many  languages  employed, 
no  one  would  think  of  reintroducing  Latin.* 

The  facility  with  which  the  ancient  languages  lend 
themselves  to  the  expression  of  new  ideas  is  evidenced 
by  the  fact  that  the  great  majority  of  our  scientific 
ideas,  as  survivals  of  this  period  of  Latin  intercourse, 
bear  Latin  and  Greek  designations,  while  in  great 
measure  scientific  ideas  are  even  now  invested  with 
names  from  these  sources.  But  to  deduce  from  the 
existence  and  use  of  such  terms  the  necessity  of  still 
learning  Latin  and  Greek  on  the  part  of  all  who  em- 
ploy them  is  carrying  the  conclusion  too  far.  All  terms, 
appropriate  and  inappropriate, — and  there  are  a  large 
number  of  inappropriate  and  monstrous  combinations 
in  science, — rest  on  convention.  The  essential  thing 
is,  that  people  should  associate  with  the  sign  the  pre- 
cise idea  that  is  designated  by  it.  It  matters  little 
whether  a  person  can  correctly  derive  the  words  tele- 
graph, tangent,  ellipse,  evolute,  etc.,  if  the  correct  idea 

*  There  is  a  peculiar  irony  of  fate  in  the  fact  that  while  Leibnitz  was  cast- 
ing about  for  a  new  vehicle  of  universal  linguistic  intercourse,  the  Latin  lan- 
guage which  still  subserved  this  purpose  the  best  of  all,  was  dropping  more 
and  more  out  of  use,  and  that  Leibnitz  himself  contributed  not  the  least  to 
this  result. 


ON  THE  CLASSICS  AND  THE  SCIENCES.         343 

is  present  in  his  mind  when  he  uses  them.  On  the 
other  hand,  no  matter  how  well  he  may  know  their  ety- 
mology, his  knowledge  will  be  of  little  use  to  him  if 
the  correct  idea  is  absent.  Ask  the  average  and  fairly 
educated  classical  scholar  to  translate  a  few  lines  for 
you  from  Newton's  Principia,  or  from  Huygens's  Ho- 
rologium,  and  you  will  discover  at  once  what  an  ex- 
tremely subordinate  role  the  mere  knowledge  of  lan- 
guage plays  in  such  things.  Without  its  associated 
thought  a  word  remains  a  mere  sound.  The  fashion  of 
employing  Greek  and  Latin  designations — for  it  can 
be  termed  nothing  else — has  a  natural  root  in  history; 
it  is  impossible  for  the  practice  to  disappear  suddenly, 
but  it  has  fallen  of  late  considerably  into  disuse.  The 
terms  gas,  ohm,  Ampere,  volt,  etc.,  are  in  international 
use,  but  they  are  not  Latin  nor  Greek.  Only  the  per- 
son who  rates  the  unessential  and  accidental  husk 
higher  than  its  contents,  can  speak  of  the  necessity  of 
learning  Latin  or  Greek  for  such  reasons,  to  say  noth- 
ing of  spending  eight  or  ten  years  on  the  task.  Will 
not  a  dictionary  supply  in  a  few  seconds  all  the  in- 
formation we  wish  on  such  subjects?* 

*As  a  rule,  the  human  brain  is  too  much,  and  wrongly,  burdened  with 
things  which  might  be  more  conveniently  and  accurately  preserved  in  books 
where  they  could  be  found  at  a  moment's  notice.  In  a  recent  letter  to  me 
from  DQsseldorf,  Judge  Hartwich  writes  : 

"A  host  of  words  exist  which  are  out  and  out  Latin  or  Greek,  yet  are  em- 
'  ployed  with  perfect  correctness  by  people  of  good  education  who  never  had 
'  the  good  luck  to  be  taught  the  ancient  languages.  For  example,  words  like 
' '  dynasty.'.  .  .  The  child  learns  such  words  as  parts  of  the  common  stock  of 
'speech,  or  even  as  parts  of  his  mother-tongue,  just  as  he  does  the  words 
' '  father,'  '  mother,'  '  bread,'  '  milk.'  Does  the  ordinary  mortal  know  tbe  ety- 
'  mology  of  these  Saxon  words  ?  Did  it  not  require  the  almost  incredible 


344         ON  THE  CLASSICS  AND  THE  SCIENCES. 

It  is  indisputable  that  our  modern  civilisation  took 
up  the  threads  of  the  ancient  civilisation,  that  at 
many  points  it  begins  where  the  latter  left  off,  and 
that  centuries  ago  the  remains  of  the  ancient  culture 
were  the  only  culture  existing  in  Europe.  Then,  of 
course,  a  classical  education  really  was  the  liberal  edu- 
cation, the  higher  education,  the  ideal  education,  for 
it  was  the  sole  education.  But  when  the  same  claim 
is  now  raised  in  behalf  of  a  classical  education,  it  must 
be  uncompromisingly  contested  as  bereft  of  all  foun- 
dation. For  our  civilisation  has  gradually  attained 
its  independence  ;  it  has  lifted  itself  far  above  the  an- 
cient civilisation,  and  has  entered  generally  new  direc- 
tions of  progress.  Its  note,  its  characteristic  feature, 
is  the  enlightenment  that  has  come  from  the  great 
mathematical  and  physical  researches  of  the  last  cen- 
turies, and  which  has  permeated  not  only  the  prac- 
tical arts  and  industries  but  is  also  gradually  finding 
its  way  into  all  fields  of  thought,  including  philosophy 
and  history,  sociology  and  linguistics.  Those  traces 
of  ancient  views  that  are  still  discoverable  in  philoso- 
phy, law,  art,  and  science,  operate  more  as  hindrances 
than  helps,  and  will  not  long  stand  before  the  devel- 
opment of  independent  and  more  natural  views. 


1  industry  of  the  Grimms  and  other  Teutonic  philologists  to  throw  the  merest 
•  glimmerings  of  light  upon  the  origin  and  growth  of  our  own  mother-tongue  ? 
'  Besides,  do  not  thousands  of  people  of  so-called  classical  education  use 
'  every  moment  hosts  of  words  of  foreign  origin  whose  derivation  they  do  not 
1  know  ?  Very  few  of  them  think  it  worth  while  to  look  up  such  words  in  the 
'  dictionaries,  although  they  love  to  maintain  that  people  should  study  the 
'  ancient  languages  for  the  sake  of  etymology  alone." 


ON  THE  CLASSICS  AND  THE  SCIENCES.         345 

It  ill  becomes  classical  scholars,  therefore,  to  re- 
gard themselves,  at  this  day,  as  the  educated  class 
par  excellence,  to  condemn  as  uneducated  all  persons 
who  do  not  understand  Latin  and  Greek,  to  complain 
that  with  such  people  profitable  conversations  are  not 
to  be  carried  on,  etc.  The  most  delectable  stories 
have  got  into  circulation,  illustrative  of  the  defective 
education  of  scientists  and  engineers.  A  renowned 
inquirer,  for  example,  is  said  to  have  once  announced 
his  intention  of  holding  a  free  course  of  university  lec- 
tures, with  the  word  "frustra" ;  an  engineer  who  spent 
his  leisure  hours  in  collecting  insects  is  said  to  have 
declared  that  he  was  studying  "etymology."  It  is 
true,  incidents  of  this  character  make  us  shudder  or 
smile,  according  to  our  mood  or  temperament.  But 
we  must  admit,  the  next  moment,  that  in  giving  way 
to  such  feelings  we  have  merely  succumbed  to  a  child- 
ish prejudice.  A  lack  of  tact  but  certainly  no  lack  of 
education  is  displayed  in  the  use  of  such  half-under- 
stood expressions.  Every  candid  person  will  confess 
that  there  are  many  branches  of  knowledge  about  which 
he  had  better  be  silent.  We  shall  not  be  so  unchari- 
table as  to  turn  the  tables  and  discuss  the  impression 
that  classical  scholars  might  make  on  a  scientist  or 
engineer,  in  speaking  of  science.  Possibly  many  ludi- 
crous stories  might  be  told  of  them,  and  of  far  more 
serious  import,  which  should  fully  compensate  for  the 
blunders  of  the  other  party. 

The  mutual  severity  of  judgment  which  we  have 


346         ON  THE  CLASSICS  AND  THE  SCIENCES. 

here  come  upon,  may  also  forcibly  bring  home  to  us 
how  really  scarce  a  true  liberal  culture  is.  We  may 
detect  in  this  mutual  attitude,  too,  something  of  that 
narrow,  mediaeval  arrogance  of  caste,  where  a  man 
began,  according  to  the  special  point  of  view  of  the 
speaker,  with  the  scholar,  the  soldier,  or  the  nobleman. 
Little  sense  or  appreciation  is  to  be  found  in  it  for  the 
common  task  of  humanity,  little  feeling  for  the  need  of 
mutual  assistance  in  the  great  work  of  civilisation, 
little  breadth  of  mind,  little  truly  liberal  culture. 

A  knowledge  of  Latin,  and  partly,  also,  a  knowl- 
edge of  Greek,  is  still  a  necessity  for  the  members  of 
a  few  professions  by  nature  more  or  less  directly  con- 
cerned with  the  civilisations  of  antiquity,  as  for  law- 
yers, theologians,  philologists,  historians,  and  gen- 
erally for  a  small  number  of  persons,  among  whom 
from  time  to  time  I  count  myself,  who  are  compelled 
to  seek  for  information  in  the  Latin  literature  of  the 
centuries  just  past.*  But  that  all  young  persons  in 
search  of  a  higher  education  should  pursue  for  this 
reason  Latin  and  Greek  to  such  excess ;  that  persons 
intending  to  become  physicians  and  scientists  should 
come  to  the  universities  defectively  educated,  or  even 
miseducated ;  and  that  they  should  be  compelled  to 

*  Standing  remote  from  the  legal  profession  I  should  not  have  ventured  to 
declare  that  the  study  of  Greek  was  not  necessary  for  the  jurists ;  yet  this 
view  was  taken  in  the  debate  that  followed  this  lecture  by  professional  jurists 
of  high  standing.  According  to  this  opinion,  the  preparatory  education  ob- 
tained in  the  German  Realgynmasium  would  also  be  sufficient  for  the  future 
jurists  and  insufficient  only  for  theologians  and  philologists.  [In  England  and 
America  not  only  is  Greek  not  necessary,  but  the  law-Latin  is  so  peculiar  that 
even  persons  of  good  classical  education  cannot  understand  it.— TV.] 


ON  THE  CLASSICS  AND  THE  SCIENCES.        347 

come  only  from  schools  that  do  not  supply  them  with 
the  proper  preparatory  knowledge  is  going  a  little  bit 

too  far. 

* 
*  * 

After  the  conditions  which  had  given  to  the  study 
of  Latin  and  Greek  their  high  import  had  ceased  to 
exist,  the  traditional  curriculum,  naturally,  was  re- 
tained. Then,  the  different  effects  of  this  method  of 
education,  good  and  bad,  which  no  one  had  thought  of 
at  its  introduction,  were  realised  and  noted.  As  nat- 
ural, too,  was  it  that  those  who  had  strong  interests 
in  the  preservation  of  these  studies,  from  knowing  no 
others  or  from  living  by  them,  or  for  still  other  rea- 
sons, should  emphasise  the  good  re.sults  of  such  in- 
struction. They  pointed  to  the  good  effects  as  if  they 
had  been  consciously  aimed  at  by  the  method  and  could 
be  attained  only  through  its  agency. 

One  real  benefit  that  students  might  derive  from 
a  rightly  conducted  course  in  the  classics  would  be 
the  opening  up  of  the  rich  literary  treasures  of  an- 
tiquity, and  intimacy  with  the  conceptions  and  views 
of  the  world  held  by  two  advanced  nations.  A  person 
who  has  read  and  understood  the  Greek  and  Roman 
authors  has  felt  and  experienced  more  than  one  who  is 
restricted  to  the  impressions  of  the  present.  He  sees 
how  men  placed  in  different  circumstances  judge  quite 
differently  of  the  same  things  from  what  we  do  to-day. 
His  own  judgments  will  be  rendered  thus  more  inde- 
pendent. Again,  the  Greek  and  Latin  authors  are  indis- 


34»         ON  THE  CLASSICS  AND  THE  SCIENCES. 

putably  a  rich  fountain  of  recreation,  of  enlightenment, 
and  of  intellectual  pleasure  after  the  day's  toil,  and 
the  individual,  not  less  than  civilised  humanity  gen- 
erally, will  remain  grateful  to  them  for  all  time.  Who 
does  not  recall  with  pleasure  the  wanderings  of  Ulys- 
ses, who  does  not  listen  joyfully  to  the  simple  narra- 
tives of  Herodotus,  who  would  ever  repent  of  having 
made  the  acquaintance  of  Plato's  Dialogues,  or  of 
having  tasted  Lucian's  divine  humor?  Who  would 
give  up  the  glances  he  has  obtained  into  the  private 
life  of  antiquity  from  Cicero's  letters,  from  Plautus  or 
Terence?  To  whom  are  not  the  portraits  of  Suetonius 
undying  reminiscences?  Who,  in  fact,  would  throw 
away  any  knowledge  he  had  once  gained  ? 

Yet  people  who  draw  from  these  sources  only,  who 
know  only  this  culture,  have  surely  no  right  to  dog- 
matise about  the  value  of  some  other  culture.  As  ob- 
jects of  research  for  individuals,  this  literature  is  ex- 
tremely valuable,  but  it  is  a  different  question  whether 
it  is  equally  valuable  as  the  almost  exclusive  means  of 
education  of  our  youth. 

Do  not  other  nations  and  other  literatures  exist 
from  which  we  ought  to  learn  ?  Is  not  nature  herself 
our  first  school-mistress?  Are  our  highest  models  al- 
ways to  be  the  Greeks,  with  their  narrow  provinciality 
of  mind,  that  divided  the  world  into  "Greeks  and  bar- 
barians," with  their  superstitions,  with  their  eternal 
questioning  of  oracles  ?  Aristotle  with  his  incapacity 
to  learn  from  facts,  with  his  word-science  ;  Plato  with 


ON  THE  CLASSICS  AND  THE  SCIENCES.         349 

his  heavy,  interminable  dialogues,  with  his  barren,  at 
times  childish,  dialectics — are  they  unsurpassable  ?  * 
The  Romans  with  their  apathy,  their  pompous  exter- 
nality, set  off  by  fulsome  and  bombastic  phrases,  with 
their  narrow  minded,  philistine  philosophy,  with  their 
frenzied  sensuality,  with  their  cruel  and  bestial  indul- 
gence in  animal  and  man  baiting,  with  their  outrageous 
maltreatment  and  plundering  of  their  subjects — are 
they  patterns  worthy  of  imitation  ?  Or  shall,  perhaps, 
our  science  edify  itself  with  the  works  of  Pliny  who 
cites  midwives  as  authorities  and  himself  stands  on 
their  point  of  view? 

Besides,  if  an  acquaintance  with  the  ancient  world 
really  were  attained,  we  might  come  to  some  settle- 
ment with  the  advocates  of  classical  education.  But  it 
is  words  and  forms,  and  forms  and  words  only,  that 
are  supplied  to  our  youth ;  and  even  collateral  sub- 
jects are  forced  into  the  strait-jacket  of  the  same 
rigid  method  and  made  a  science  of  words,  sheer  feats 
of  mechanical  memory.  Really,  we  feel  ourselves  set 
back  a  thousand  years  into  the  dull  cloister-cells  of  the 
Middle  Ages. 

This  must  be  changed.     It  is  possible  to  get  ac- 

*  In  emphasising  here  the  weak  sides  of  the  writings  of  Plato  and  Aristotle, 
forced  on  my  attention  while  reading  them  in  German  translations,  I,  of 
course,  have  no  intention  of  underrating  the  great  merits  and  the  high  his- 
torical importance  of  these  two  men.  Their  importance  must  not  be  meas- 
ured by  the  fact  that  our  speculative  philosophy  still  moves  to  a  great  extent 
in  their  paths  of  thought.  The  more  probable  conclusion  is  that  this  branch 
has  made  very  little  progress  in  the  last  two  thousand  years.  Natural  science 
also  was  implicated  for  centuries  in  the  meshes  of  the  Aristotelian  thought, 
and  owes  its  rise  mainly  to  having  thrown  off  those  fetters. 


35o        ON  THE  CLASSICS  AND  THE  SCIENCES. 

quainted  with  the  views  of  the  Greeks  and  Romans  by 
a  shorter  road  than  the  intellect  deadening  process 
of  eight  or  ten  years  of  declining,  conjugating,  analys- 
ing, and  extemporisation.  There  are  to-day  plenty  of 
educated  persons  who  have  acquired  through  good 
translations  vivider,  clearer,  and  more  just  views  of 
classical  antiquity  than  the  graduates  of  our  gymna- 
siums and  colleges.* 

For  us  moderns,  the  Greeks  and  the  Romans  are 
simply  two  objects  of  archaeological  and  historical  re- 
search like  all  others.  If  we  put  them  before  our 
youth  in  fresh  and  living  pictures,  and  not  merely  in 
words  and  syllables,  the  effect  will  be  assured.  We 
derive  a  totally  different  enjoyment  from  the  Greeks 
when  we  approach  them  after  a  study  of  the  results 
of  modern  research  in  the  history  of  civilisation.  We 
read  many  a  chapter  of  Herodotus  differently  when  we 
attack  his  works  equipped  with  a  knowledge  of  natural 
science,  and  with  information  about  the  stone  age  and 
the  lake-dwellers.  What  our  classical  institutions  pre- 
tend to  give  can  and  actually  will  be  given  to  our  youth 
with  much  more  fruitful  results  by  competent  historical 
instruction,  which  must  supply,  not  names  and  num- 
bers alone,  nor  the  mere  history  of  dynasties  and  wars, 
but  be  in  every  sense  of  the  word  a  true  history  of 
civilisation. 

*  I  would  not  for  a  moment  contend  that  we  derive  exactly  the  same  profit 
from  reading  a  Greek  author  in  a  translation  as  from  reading  him  in  the  orig- 
inal ;  but  the  difference,  the  excess  of  gain  in  the  second  case,  appears  to  me, 
and  probably  will  to  most  men  who  are  not  professional  philologists,  to  be 
too  dearly  bought  with  the  expenditure  of  eight  years  of  valuable  time. 


ON  THE  CLASSICS  AND  THE  SCIENCES.         351 

The  view  still  widely  prevails  that  although  all 
"higher,  ideal  culture,"  all  extension  of  our  view  of 
the  world,  is  acquired  by  philological  and  in  a  lesser 
degree  by  historical  studies,  still  the  mathematics  and 
natural  sciences  should  not  be  neglected  on  account 
of  their  usefulness.  This  is  an  opinion  to  which  I  must 
refuse  my  assent.  It  were  strange  if  man  could  learn 
more,  could  draw  more  intellectual  nourishment,  from 
the  shards  of  a  few  old  broken  jugs,  from  inscribed 
stones,  or  yellow  parchments,  than  from  all  the  rest 
of  nature.  True,  man  is  man's  first  concern,  but  he 
is  not  his  sole  concern. 

In  ceasing  to  regard  man  as  the  centre  of  the  world ; 
in  discovering  that  the  earth  is  a  top  whirled  about 
the  sun,  which  speeds  off  with  it  into  infinite  space; 
in  finding  that  in  the  fixed  stars  the  same  elements 
exist  as  on  earth ;  in  meeting  everywhere  the  same 
processes  of  which  the  life  of  man  is  merely  a  vanish- 
ingly  small  part — in  such  things,  too,  is  a  widening  of 
our  view  of  the  world,  and  edification,  and  poetry. 
There  are  here  perhaps  grander  and  more  significant 
facts  than  the  bellowing  of  the  wounded  Ares,  or  the 
charming  island  of  Calypso,  or  the  ocean-stream  en- 
girdling the  earth.  He  only  should  speak  of  the  rela- 
tive value  of  these  two  domains  of  thought,  of  their 
poetry,  who  knows  both. 

The  "utility"  of  physical  science  is,  in  a  measure, 
only  a  collateral  product  of  that  flight  of  the  intellect 
which  produced  science.  No  one,  however,  should 


352         ON  THE  CLASSICS  AND  THE  SCIENCES, 

underrate  the  utility  of  science  who  has  shared  in  the 
realisation  by  modern  industrial  art  of  the  Oriental 
world  of  fables,  much  less  one  upon  whom  those  treas- 
ures have  been  poured,  as  it  were,  from  the  fourth  di- 
mension, without  his  aid  or  understanding. 

Nor  may  we  believe  that  science  is  useful  only  to 
the  practical  man.  Its  influence  permeates  all  our  af- 
fairs, our  whole  life ;  everywhere  its  ideas  are  decisive. 
How  differently  does  the  jurist,  the  legislator,  or  the 
political  economist  think,  who  knows,  for  example, 
that  a  square  mile  of  the  most  fertile  soil  can  support 
with  the  solar  heat  annually  consumed  only  a  definite 
number  of  human  beings,  which  no  art  or  science  can 
increase.  Many  economical  theories,  which  open  new 
air-paths  of  progress,  air-paths  in  the  literal  sense  of 
the  word,  would  be  made  impossible  by  such  knowl- 
edge. 

*  * 

The  eulogists  of  classical  education  love  to  empha- 
sise the  cultivation  of  taste  which  comes  from  employ- 
ment with  the  ancient  models.  I  candidly  confess 
that  there  is  something  absolutely  revolting  in  this  to 
me.  To  form  the  taste,  then,  our  youths  must  sacrifice 
ten  years  of  their  life  !  Luxury  takes  precedence  over 
necessity.  Have  the  future  generations,  in  the  face 
of  the  difficult  problems,  the  great  social  questions, 
which  they  must  meet,  and  that  with  strengthened 
mind  and  heart,  no  more  important  duties  to  fulfil  than 
these  ? 


ON  THE  CLASSICS  AND  THE  SCIENCES.        353 

But  let  us  assume  that  this  end  were  desirable. 
Can  taste  be  formed  by  rules  and  precepts  ?  Do  not 
ideals  of  beauty  change  ?  Is  it  not  a  stupendous  ab- 
surdity to  force  one's  self  artificially  to  admire  things 
which,  with  all  their  historical  interest,  with  all  their 
beauty  in  individual  points,  are  for  the  most  part 
foreign  to  the  rest  of  our  thoughts  and  feelings,  pro- 
vided we  have  such  of  our  own.  A  nation  that  is 
truly  such,  has  its  own  taste  and  will  not  go  to  others 
for  it.  And  every  individual  perfect  man  has  his  own 
taste.* 

And  what,  after  all,  does  this  cultivation  of  taste 
consist  in  ?  In  the  acquisition  of  the  personal  literary 
style  of  a  few  select  authors  !  What  should  we  think 
of  a  people  that  would  force  its  youth  a  thousand 
years  from  now,  by  years  of  practice,  to  master  the 
tortuous  or  bombastic  style  of  some  successful  lawyer 
or  politician  of  to-day?  Should  we  not  justly  accuse 
them  of  a  woful  lack  of  taste  ? 

The  evil  effects  of  this  imagined  cultivation  of  the 

*  "  The  temptation,"  Judge  Hartwich  writes,  "  to  regard  the  '  taste '  of  the 
"ancients  as  so  lofty  and  unsurpassable  appears  to  me  to  have  its  chief  origin 
"in  the  fact  that  the  ancients  were  unexcelled  in  the  representation  of  the 
"nude.  First,  by  their  unremitting  care  of  the  human  body  they  produced 
"splendid  models;  and  secondly,  in  their  gymnasiums  and  in  their  athletic 
"  games  they  had  these  models  constantly  before  their  eyes.  No  wonder,  then, 
"  that  their  statues  still  excite  our  admiration  t  For  the  form,  the  ideal  of  the 
"  human  body  has  not  changed  in  the  course  of  the  centuries.  But  with  intel- 
"lectual  matters  it  is  totally  different ;  they  change  from  century  to  century, 
"nay,  from  decennium  to  decennium.  It  is  very  natural  now,  that  people 
"should  unconsciously  apply  what  is  thus  so  easily  seen,  namely,  the  works  of 
"sculpture,  as  a  universal  criterion  of  the  highly  developed  taste  of  the  an- 
"  cients-a  fallacy  against  which  people  cannot,  in  my  judgment,  be  too  strongly 
"warned." 


354         ON  THE  CLASSICS  AND  THE  SCIENCES. 

taste  find  expression  often  enough.  The  young  savant 
who  regards  the  composition  of  a  scientific  essay  as  a 
rhetorical  exercise  instead  of  a  simple  and  unadorned 
presentation  of  the  facts  and  the  truth,  still  sits  uncon- 
sciously on  the  school-bench,  and  still  unwittingly  rep- 
resents the  point  of  view  of  the  Romans,  by  whom  the 
elaboration  of  speeches  was  regarded  as  a  serious  sci- 
entific (!)  employment. 

* 
*  * 

Far  be  it  from  me  to  underrate  the  value  of  the  de- 
velopment of  the  instinct  of  speech  and  of  the  increased 
comprehension  of  our  own  language  which  comes  from 
philological  studies.  By  the  study  of  a  foreign  lan- 
guage, especially  of  one  which  differs  widely  from  ours, 
the  signs  and  forms  of  words  are  first  clearly  distin- 
guished from  the  thoughts  which  they  express.  Words 
of  the  closest  possible  correspondence  in  different  lan- 
guages never  coincide  absolutely  with  the  ideas  they 
stand  for,  but  place  in  relief  slightly  different  aspects 
of  the  same  thing,  and  by  the  study  of  language  the 
attention  is  directed  to  these  shades  of  difference.  But 
it  would  be  far  from  admissible  to  contend  that  the 
study  of  Latin  and  Greek  is  the  most  fruitful  and  nat- 
ural, let  alone  the  only,  means  of  attaining  this  end. 
Any  one  who  will  give  himself  the  pleasure  of  a  few 
hours'  companionship  with  a  Chinese  grammar  ;  who 
will  seek  to  make  clear  to  himself  the  mode  of  speech 
and  thought  of  a  people  who  never  advanced  as  far  as 
the  analysis  of  articulate  sounds,  but  stopped  at  the 


ON  THE  CLASSICS  AND  THE  SCIENCES.         355 

analysis  of  syllables,  to  whom  our  alphabetical  char- 
acters, therefore,  are  an  inexplicable  puzzle,  and  who 
express  all  their  rich  and  profound  thoughts  by  means 
of  a  few  syllables  with  variable  emphasis  and  position, 
— such  a  person,  perhaps,  will  acquire  new,  and  ex- 
tremely elucidative  ideas  upon  the  relation  of  lan- 
guage and  thought.  But  should  our  children,  there- 
fore, study  Chinese  ?  Certainly  not.  No  more,  then, 
should  they  be  burdened  with  Latin,  at  least  in  the 
measure  they  are. 

It  is  a  beautiful  achievement  to  reproduce  a  Latin 
thought  in  a  modern  language  with  the  maximum  fidel- 
ity of  meaning  and  expression  —  for  the  translator. 
Moreover,  we  shall  be  very  grateful  to  the  translator 
for  his  performance.  But  to  demand  this  feat  of  every 
educated  man,  without  consideration  of  the  sacrifice  of 
time  and  labor  which  it  entails,  is  unreasonable.  And 
for  this  very  reason,  as  classical  teachers  admit,  that 
ideal  is  never  perfectly  attained,  except  in  rare  cases 
with  scholars  poss'essed  of  special  talents  and  great 
industry.  Without  slurring,  therefore,  the  high  im- 
portance of  the  study  of  the  ancient  languages  as  a 
profession,  we  may  yet  feel  sure  that  the  instinct  for 
speech  which  is  part  of  every  liberal  education  can, 
and  must,  be  acquired  in  a  different  way.  Should  we, 
indeed,  be  forever  lost  if  the  Greeks  had  not  lived  be- 
fore us  ? 

The  fact  is,  we  must  carry  our  demands  further 
than  the  representatives  of  classical  philology.  We 


356        ON  THE  CLASSICS  AND  THE  SCIENCES. 

must  ask  of  every  educated  man  a  fair  scientific  con- 
ception of  the  nature  and  value  of  language,  of  the 
formation  of  language,  of  the  alteration  of  the  mean- 
ing of  roots,  of  the  degeneration  of  fixed  forms  of 
speech  to  grammatical  forms,  in  brief,  of  all  the  main 
results  of  modern  comparative  philology.  We  should 
judge  that  this  were  attainable  by  a  careful  study  of 
our  mother  tongue  and  of  the  languages  next  allied  to 
it,  and  subsequently  of  the  more  ancient  tongues  from 
which  the  former  are  derived.  If  any  one  object  that 
this  is  too  difficult  and  entails  too  much  labor,  I  should 
advise  such  a  person  to  place  side  by  side  an  English, 
a  Dutch,  a  Danish,  a  Swedish,  and  a  German  Bible,  and 
to  compare  a  few  lines  of  them ;  he  will  be  amazed  at 
the  multitude  of  suggestions  that  offer  themselves.* 
In  fact,  I  believe  that  a  really  progressive,  fruitful,  ra- 
tional, and  instructive  study  of  languages  can  be  con- 
ducted only  on  this  plan.  Many  of  my  audience  will 
remember,  perhaps,  the  bright  and  encouraging  effect, 
like  that  of  a  ray  of  sunlight  on  a"  gloomy  day,  which 
the  meagre  and  furtive  remarks  on  comparative  phi- 


*  English:  "In  the  beginning  God  created  the  heaven  and  the  earth. 
"And  the  earth  was  without  form  and  void  ;  and  darkness  was  upon  the  face 
"  of  the  deep.  And  the  spirit  of  God  moved  upon  the  face  of  the  waters." — 
Dutch  :  "  In  bet  begin  schiep  God  den  hemel  en  de  aarde.  De  aarde  nu  was 
"  woest  en  ledig,  en  duisternis  was  op  den  afgrond  ;  en  de  Geest  Godszwefde 
"op  de  wateren."— Danish  :  "  I  Begyndelsen  skabte  Gud  Himmelen  og  Jor- 
"den.  Og  Jorden  var  ode  og  torn,  og  der  var  morkt  ovenover  Afgrunden,  og 
"Guds  Aand  svoevede  ovenover  Vandene." — Swedish:  "I  begynnelsen  ska- 
"  pade  Gud  Himmel  och  Jord.  Och  Jorden  war  Ode  och  torn,  och  mOrker  war 
"  pa  djupet,  och  Gods  Ande  swafde  Cfwer  wattnet." — German:  "Am  Anfang 
"schuf  Gott  Himmel  und  Erde.  Und  die  Erde  war  wQst  und  leer,  und  es  war 
"finster  auf  der  Tiefe  ;  und  der  Geist  Gottes  schwebte  auf  dem  Wasser. " 


ON  THE  CLASSICS  AND  THE  SCIENCES.        357 

lology  in   Curtius's  Greek  grammar  wrought  in  thai 
barren  and  lifeless  desert  of  verbal  quibbles. 

* 
*  * 

The  principal  result  obtained  by  the  present  method 
of  studying  the  ancient  languages  is  that  which  comes 
from  the  student's  employment  with  their  complicated 
grammars.  It  consists  in  the  sharpening  of  the  atten- 
tion and  in  the  exercise  of  the  judgment  by  the  prac- 
tice of  subsuming  special  cases  under  general  rules, 
and  of  distinguishing  between  different  cases.  Ob- 
viously, the  same  result  can  be  reached  by  many  other 
methods ;  for  example,  by  difficult  games  of  cards. 
Every  science,  the  mathematics  and  the  physical  sci- 
ences included,  accomplish  as  much,  if  not  more,  in 
this  disciplining  of  the  judgment.  In  addition,  the 
matter  treated  by  those  sciences  has  a  much  higher  in- 
trinsic interest  for  young  people,  and  so  engages  spon- 
taneously their  attention ;  while  on  the  other  hand  they 
are  elucidative  and  useful  in  other  directions  in  which 
grammar  can  accomplish  nothing. 

Who  cares,  so  far  as  the  matter  of  it  is  concerned, 
whether  we  say  hominum  or  hominorum  in  the  genitive 
plural,  interesting  as  the  fact  may  be  for  the  philolo- 
gist? And  who  would  dispute  that  the  intellectual 
need  of  causal  insight  is  awakened  not  by  grammar 
but  by  the  natural  sciences  ? 

It  is  not  our  intention,  therefore,  to  gainsay  in  the 
least  the  good  influence  which  the  study  of  Latin  and 
Greek  grammar  also  exercises  on  the  sharpening  of  the 


358          ON  THE  CLASSICS  AND   THE  SCIENCES. 

judgment.  In  so  far  as  the  study  of  words  as  such 
must  greatly  promote  lucidity  and  accuracy  of  ex- 
pression, in  so  far  as  Latin  and  Greek  are  not  yet 
wholly  indispensable  to  many  branches  of  knowledge, 
we  willingly  concede  to  them  a  place  in  our  schools, 
but  would  demand  that  the  disproportionate  amount  of 
time  allotted  to  them,  wrongly  withdrawn  from  other 
useful  studies,  should  be  considerably  curtailed.  That 
in  the  end  Latin  and  Greek  will  not  be  employed  as 
the  universal  means  of  education,  we  are  fully  con- 
vinced. They  will  be  relegated  to  the  closet  of  the 
scholar  or  professional  philologist,  and  gradually  make 
way  for  the  modern  languages  and  the  modern  science 
of  language. 

Long  ago  Locke  reduced  to  their  proper  limits  the 
exaggerated  notions  which  obtained  of  the  close  con- 
nexion of  thought  and  speech,  of  logic  and  grammar, 
and  recent  investigators  have  established  on  still  surer 
foundations  his  views.  How  little  a  complicated  gram- 
mar is  necessary  for  expressing  delicate  shades  of 
thought  is  demonstrated  by  the  Italians  and  French, 
who,  although  they  have  almost  totally  discarded  the 
grammatical  redundancies  of  the  Romans,  are  yet  not 
surpassed  by  the  latter  in  accuracy  of  thought,  and 
whose  poetical,  but  especially  whose  scientific  litera- 
ture, as  no  one  will  dispute,  can  bear  favorable  com- 
parison with  the  Roman. 

Reviewing  again  the  arguments  advanced  in  favor 
of  the  study  of  the  ancient  languages,  we  are  obliged 


ON  THE  CLASSICS  AND  THE  SCIENCES.         359 

to  say  that  in  the  main  and  as  applied  to  the  present, 
they  are  wholly  devoid  of  force.  In  so  far  as  the 
aims  which  this  study  theoretically  pursues  are  still 
worthy  of  attainment,  they  appear  to  us  as  altogether 
too  narrow,  and  are  surpassed  in  this  only  by  the 
means  employed.  As  almost  the  sole,  indisputable  re- 
sult of  this  study  we  must  count  the  increase  of  the 
student's  skill  and  precision  in  expression.  One  in- 
clined to  be  uncharitable  might  say  that  our  gymna- 
siums and  classical  academies  turn  out  men  who  can 
speak  and  write,  but,  unfortunately,  have  little  to  write 
or  speak  about.  Of  that  broad,  liberal  view,  of  that 
famed  universal  culture,  which  the  classical  curriculum 
is  supposed  to  yield,  serious  words  need  not  be  lost. 
This  culture  might,  perhaps,  more  properly  be  termed 
the  contracted  or  lopsided  culture. 


While  considering  the  study  of  languages  we  threw 
a  few  side  glances  at  mathematics  and  the  natural  sci- 
ences. Let  us  now  inquire  whether  these,  as  branches 
of  study,  cannot  accomplish  much  that  is  to  be  attained 
in  no  other  way.  I  shall  meet  with  no  contradiction 
when  I  say  that  without  at  least  an  elementary  mathe- 
matical and  scientific  education  a  man  remains  a  total 
stranger  in  the  world  in  which  he  lives,  a  stranger  in 
the  civilisation  of  the  time  that  bears  him.  Whatever 
he  meets  in  nature,  or  in  the  industrial  world,  either 
does  not  appeal  to  him  at  all,  from  his  having  neither 


360         ON  THE  CLASSICS  AND  THE  SCIENCES. 

eye  nor  ear  for  it,  or  it  speaks  to  him  in  a  totally  unin- 
telligible language. 

A  real  understanding  of  the  world  and  its  civilisa- 
tion, however,  is  not  the  only  result  of  the  study  of 
mathematics  and  the  physical  sciences.  Much  more 
essential  for  the  preparatory  school  is  the  formal  cul- 
tivation which  comes  from  these  studies,  the  strength- 
ening of  the  reason  and  the  judgment,  the  exercise 
of  the  imagination.  Mathematics,  physics,  chemistry, 
and  the  so-called  descriptive  sciences  are  so  much 
alike  in  this  respect,  that,  apart  from  a  few  points,  we 
need  not  separate  them  in  our  discussion. 

Logical  sequence  and  continuity  of  ideas,  so  neces- 
sary for  fruitful  thought,  are/ar  excellence  the  results  of 
mathematics ;  the  ability  to  follow  facts  with  thoughts, 
that  is,  to  observe  or  collect  experiences,  is  chiefly  de- 
veloped by  the  natural  sciences.  Whether  we  notice 
that  the  sides  and  the  angles  of  a  triangle  are  connected 
in  a  definite  way,  that  an  equilateral  triangle  possesses 
certain  definite  properties  of  symmetry,  or  whether  we 
notice  the  deflexion  of  a  magnetic  needle  by  an  elec- 
tric current,  the  dissolution  of  zinc  in  diluted  sulphuric 
acid,  whether  we  remark  that  the  wings  of  a  butterfly 
are  slightly  colored  on  the  under,  and  the  fore-wings 
of  the  moth  on  the  upper,  surface  :  indiscriminately 
here  we  proceed  from  observations,  from  individual 
acts  of  immediate  intuitive  knowledge.  The  field  of 
observation  is  more  restricted  and  lies  closer  at  hand 
in  mathematics ;  it  is  more  varied  and  broader  but 


ON  THE  CLASSICS  AND  THE  SCIENCES.         361 

more  difficult  to  compass  in  the  natural  sciences.  The 
essential  thing,  however,  is  for  the  student  to  learn  to 
make  observations  in  all  these  fields.  The  philosophi- 
cal question  whether  our  acts  of  knowledge  in  mathe- 
matics are  of  a  special  kind  is  here  of  no  importance 
for  us.  It  is  true,  of  course,  that  the  observation  can 
be  practised  by  languages  also.  But  no  one,  surely, 
will  deny,  that  the  concrete,  living  pictures  pre- 
sented in  the  fields  just  mentioned  possess  different 
and  more  powerful  attractions  for  the  mind  of  the 
youth  than  the  abstract  and  hazy  figures  which  lan- 
guage offers,  and  on  which  the  attention  is  certainly  not 
so  spontaneously  bestowed,  nor  with  such  good  re- 
sults.* 

Observation  having  revealed  the  different  proper- 
ties of  a  given  geometrical  or  physical  object,  it  is  dis- 
covered that  in  many  cases  these  properties  depend  in 
some  way  upon  one  another.  This  interdependence 
of  properties  (say  that  of  equal  sides  and  equal  angles 
at  the  base  of  a  triangle,  the  relation  of  pressure  to 
motion,)  is  nowhere  so  distinctly  marked,  nowhere  is 
the  necessity  and  permanency  of  the  interdependence 
so  plainly  noticeable,  as  in  the  fields  mentioned. 
Hence  the  continuity  and  logical  consequence  of  the 
ideas  which  we  acquire  in  those  fields.  The  relative 
simplicity  and  perspicuity  of  geometrical  and  phys- 
ical relations  supply  here  the  conditions  of  natural  and 

*  Compare  Herzen's  excellent  remarks,  Dt  feuteigntment  itcondairt  dan* 
la  Suisse  romande.  Lausanne,  1886. 


362          ON  THE  CLASSICS  AND  THE  SCIENCES. 

easy  progress.  Relations  of  equal  simplicity  are  not 
met  with  in  the  fields  which  the  study  of  language 
opens  up.  Many  of  you,  doubtless,  have  often  won- 
dered at  the  little  respect  for  the  notions  of  cause  and 
effect  and  their  connexion  that  is  sometimes  found 
among  professed  representatives  of  the  classical  stud- 
ies. The  explanation  is  probably  to  be  sought  in  the 
fact  that  the  analogous  relation  of  motive  and  action 
familiar  to  them  from  their  studies,  presents  nothing 
like  the  clear  simplicity  and  determinateness  that  the 
relation  of  cause  and  effect  does. 

That  perfect  mental  grasp  of  all  possible  cases, 
that  economical  order  and  organic  union  of  the  thoughts 
which  comes  from  it,  which  has  grown  for  every  one 
who  has  ever  tasted  it  a  permanent  need  which  he 
seeks  to  satisfy  in  every  new  province,  can  be  developed 
only  by  employment  with  the  relative  simplicity  of 
mathematical  and  scientific  investigations. 

When  a  set  of  facts  comes  into  apparent  conflict 
with  another  set  of  facts,  and  a  problem  is  presented, 
its  solution  consists  ordinarily  in  a  more  refined  dis- 
tinction or  in  a  more  extended  view  of  the  facts,  as 
may  be  aptly  illustrated  by  Newton's  solution  of  the 
problem  of  dispersion.  When  a  new  mathematical  or 
scientific  fact  is  demonstrated,  or  explained,  such  demon- 
stration also  rests  simply  upon  showing  the  connex- 
ion of  the  new  fact  with  the  facts  already  known  ;  for 
example,  that  the  radius  of  a  circle  can  be  laid  off  as 
chord  exactly  six  times  in  the  circle  is  explained  or 


ON  THE  CLASSICS  AND  THE  SCIENCES,         363 

proved  by  dividing  the  regular  hexagon  inscribed  in 
the  circle  into  equilateral  triangles.  That  the  quantity 
of  heat  developed  in  a  second  in  a  wire  conveying  an 
electric  current  is  quadrupled  on  the  doubling  of  the 
strength  of  the  current,  we  explain  from  the  doubling  of 
the  fall  of  the  potential  due  to  the  doubling  of  the 
current's  intensity,  as  also  from  the  doubling  of  the 
quantity  flowing  through,  in  a  word,  from  the  quad- 
rupling of  the  work  done.  In  point  of  principle,  ex- 
planation and  direct  proof  do  not  differ  much. 

He  who  solves  scientifically  a  geometrical,  phys- 
ical, or  technical  problem,  easily  remarks  that  his 
procedure  is  a  methodical  mental  quest,  rendered  pos- 
sible by  the  economical  order  of  the  province — a  sim- 
plified purposeful  quest  as  contrasted  with  unmethod- 
ical, unscientific  guess-work.  The  geometer,  for  ex- 
ample, who  has  to  construct  a  circle  touching  two  given 
straight  lines,  casts  his  eye  over  the  relations  of  sym- 
metry of  the  desired  construction,  and  seeks  the  centre 
of  his  circle  solely  in  the  line  of  symmetry  of  the  two 
straight  lines.  The  person  who  wants  a  triangle  of 
which  two  angles  and  the  sum  of  the  sides  are  given, 
grasps  in  his  mind  the  determinateness  of  the  form  of 
this  triangle  and  restricts  his  search  for  it  to  a  certain 
group  of  triangles  of  the  same  form.  Under  very  dif- 
ferent circumstances,  therefore,  the  simplicity,  the  in- 
tellectual perviousness,  of  the  subject-matter  of  mathe- 
matics and  natural  science  is  felt,  and  promotes  both 
the  discipline  and  the  self-confidence  of  the  reason. 


364          ON  THE  CLASSICS  AND  THE  SCIENCES. 

Unquestionably,  much  more  will  be  attained  by  in- 
struction in  the  mathematics  and  the  natural  sciences 
than  now  is,  when  more  natural  methods  are  adopted. 
One  point  of  importance  here  is  that  young  students 
should  not  be  spoiled  by  premature  abstraction,  but 
should  be  made  acquainted  with  their  material  from 
living  pictures  of  it  before  they  are  made  to  work  with 
it  by  purely  ratiocinative  methods.  A  good  stock  of 
geometrical  experience  could  be  obtained,  for  exam- 
ple, from  geometrical  drawing  and  from  the  practical 
construction  of  models.  In  the  place  of  the  unfruitful 
method  of  Euclid,  which  is  only  fit  for  special,  re- 
stricted uses,  a  broader  and  more  conscious  method 
must  be  adopted,  as  Hankel  has  pointed  out.*  Then, 
if,  on  reviewing  geometry,  and  after  it  presents  no 
substantial  difficulties,  the  more  general  points  of  view, 
the  principles  of  scientific  method  are  placed  in  relief 
and  brought  to  consciousness,  as  Von  Nagel,f  J.  K. 
Becker,J  Mann,§  and  others  have  well  done,  fruit- 
ful results  will  be  surely  attained.  In  the  same  way, 
the  subject-matter  of  the  natural  sciences  should  be 
made  familiar  by  pictures  and  experiment  before  a 
profounder  and  reasoned  grasp  of  these  subjects  is 
attempted.  Here  the  emphasis  of  the  more  general 
points  of  view  is  to  be  postponed. 

Before  my  present  audience  it  would  be  superfluous 

*  Geschichte  der  Mathematik,  Leipsic,  1874. 

t  Geometristhe  Analyse,  Ulm,  1886. 

tin  his  text-books  of  elementary  mathematics. 

§  Abhandlungen  aus  dent  Gebiete  der  Mathematik,  Wfirzburg.  1883. 


ON  THE  CLASSICS  AND  THE  SCIENCES.         365 

for  me  to  contend  further  that  mathematics  and  nat- 
ural science  are  justified  constituents  of  a  sound  edu- 
cation,— a  claim  that  even  philologists,  after  some 
resistance,  have  conceded.  Here  I  may  count  upon 
assent  when  I  say  that  mathematics  and  the  natural 
sciences  pursued  alone  as  means  of  instruction  yield  a 
richer  education  in  matter  and  form,  a  more  general 
education,  an  education  better  adapted  to  the  needs 
and  spirit  of  the  time, — than  the  philological  branches 
pursued  alone  would  yield. 

But  how  shall  this  idea  be  realised  in  the  curricula 
of  our  intermediate  educational  institutions?  It  is  un- 
questionable in  my  mind  that  the  German  Rcalschulen 
and  Realgymnasien,  where  the  exclusive  classical  course 
is  for  the  most  part  replaced  by  mathematics,  science, 
and  modern  languages,  give  the  average  man  a  more 
timely  education  than  the  gymnasium  proper,  although 
they  are  not  yet  regarded  as  fit  preparatory  schools  for 
future  theologians  and  professional  philologists.  The 
German  gymnasiums  are  too  one-sided.  With  these 
the  first  changes  are  to  be  made ;  of  these  alone  we 
shall  speak  here.  Possibly  a  single  preparatory  school, 
suitably  planned,  might  serve  all  purposes. 

Shall  we,  then,  in  our  gymnasiums  fill  out  the  hours 
of  study  which  stand  at  our  disposal,  or  are  still  to  be 
wrested  from  the  classicists,  with  as  great  and  as  va- 
ried a  quantity  of  mathematical  and  scientific  matter 
as  possible  ?  Expect  no  such  proposition  from  me. 
No  one  will  suggest  such  a  course  who  has  himself 


366         ON  THE  CLASSICS  AND  THE  SCIENCES. 

been  actively  engaged  in  scientific  thought.  Thoughts 
can  be  awakened  and  fructified  as  a  field  is  fructified 
by  sunshine  and  rain.  But  thoughts  cannot  be  jug- 
gled out  and  worried  out  by  heaping  up  materials  and 
the  hours  of  instruction,  nor  by  any  sort  of  precepts  : 
they  must  grow  naturally  of  their  own  free  accord. 
Furthermore,  thoughts  cannot  be  accumulated  beyond 
a  certain  limit  in  a  single  head,  any  more  than  the  pro- 
duce of  a  field  can  be  increased  beyond  certain  limits. 
I  believe  that  the  amount  of  matter  necessary  for  a 
useful  education,  such  as  should  be  offered  to  all  the 
pupils  of  a  preparatory  school,  is  very  small.  If  I  had 
the  requisite  influence,  I  should,  in  all  composure,  and 
fully  convinced  that  I  was  doing  what  was  best,  first 
greatly  curtail  in  the  lower  classes  the  amount  of  mat- 
ter in  both  the  classical  and  the  scientific  courses ;  I 
should  cut  down  considerably  the  number  of  the  school 
hours  and  the  work  done  outside  the  school.  I  am 
not  with  many  teachers  of  opinion  that  ten  hours  work 
a  day  for  a  child  is  not  too  much.  I  am  convinced 
that  the  mature  men  who  offer  this  advice  so  lightly 
are  themselves  unable  to  give  their  attention  success- 
fully for  as  long  a  time  to  any  subject  that  is  new  to 
them,  (for  example,  to  elementary  mathematics  or 
physics,)  and  I  would  ask  every  one  who  thinks  the 
contrary  to  make  the  experiment  upon  himself.  Learn- 
ing and  teaching  are  not  routine  office-work  that  can 
be  kept  up  mechanically  for  long  periods.  But  even 
such  work  tires  in  the  end.  If  our  young  men  are 


ON  THE  CLASSICS  AND  THE  SCIENCES.         367 

not  to  enter  the  universities  with  blunted  and  impov- 
erished minds,  if  they  are  not  to  leave  in  the  pre- 
paratory schools  their  vital  energy,  which  they  should 
there  gather,  great  changes  must  be  made.  Waiving 
the  injurious  effects  of  overwork  upon  the  body,  the 
consequences  of  it  for  the  mind  seem  to  me  positively 
dreadful. 

I  know  of  nothing  more  terrible  than  the  poor  crea- 
tures who  have  learned  too  much.  Instead  of  that 
sound  powerful  judgment  which  would  probably  have 
grown  up  if  they  had  learned  nothing,  their  thoughts 
creep  timidly  and  hypnotically  after  words,  principles, 
and  formulae,  constantly  by  the  same  paths.  What 
they  have  acquired  is  a  spider's  web  of  thoughts  too 
weak  to  furnish  sure  supports,  but  complicated  enough 
to  produce  confusion. 

But  how  shall  better  methods  of  mathematical  and 
scientific  education  be  combined  with  the  decrease  of 
the  subject-matter  of  instruction  ?  I  think,  by  aban- 
doning systematic  instruction  altogether,  at  least  in  so 
far  as  that  is  required  of  all  young  pupils.  I  see  no 
necessity  whatever  that  the  graduates  of  our  high 
schools  and  preparatory  schools  should  be  little  phi- 
lologists, and  at  the  same  time  little  mathematicians, 
physicists,  and  botanists  ;  in  fact,  I  do  not  see  the  pos- 
sibility of  such  a  result.  I  see  in  the  endeavor  to  at- 
tain this  result,  in  which  every  instructor  seeks  for  his 
own  branch  a  place  apart  from  the  others,  the  main 
mistake  of  our  whole  system.  I  should  be  satisfied  if 


368         ON  THE  CLASSICS  AND  THE  SCIENCES. 

every  young  student  could  come  into  living  contact 
with  and  pursue  to  their  ultimate  logical  consequences 
merely  a  few  mathematical  or  scientific  discoveries. 
Such  instruction  would  be  mainly  and  naturally  asso- 
ciated with  selections  from  the  great  scientific  classics. 
A  few  powerful  and  lucid  ideas  could  thus  be  made 
to  take  root  in  the  mind  and  receive  thorough  elabora- 
tion. This  accomplished,  our  youth  would  make  a 
different  showing  from  what  they  do  to-day.* 

What  need  is  there,  for  example,  of  burdening  the 
head  of  a  young  student  with  all  the  details  of  botany  ? 
The  student  who  has  botanised  under  the  guidance  of 
a  teacher  finds  on  all  hands,  not  indifferent  things,  but 
known  or  unknown  things,  by  which  he  is  stimulated, 
and  his  gain  made  permanent.  I  express  here,  not  my 
own,  but  the  opinion  of  a  friend,  a  practical  teacher. 
Again,  it  is  not  at  all  necessary  that  all  the  matter  that 
is  offered  in  the  schools  should  be  learned.  The  best 
that  we  have  learned,  that  which  has  remained  with 
us  for  life,  outlived  the  test  of  examination.  How  can 
the  mind  thrive  when  matter  is  heaped  on  matter,  and 
new  materials  piled  constantly  on  old,  undigested  ma- 
terials? The  question  here  is  not  so  much  that  of  the 
accumulation  of  positive  knowledge  as  of  intellectual 

*  My  idea  here  is  an  appropriate  selection  of  readings  from  Galileo,  Huy- 
gens,  Newton,  etc.  The  choice  is  so  easily  made  that  there  can  be  no  ques- 
tion of  difficulties.  The  contents  would  be  discussed  with  the  students,  and 
the  original  experiments  performed  with  them.  Those  scholars  alone  should 
receive  this  instruction  in  the  upper  classes  who  did  not  look  forward  to  sys- 
tematical instruction  in  the  physical  sciences.  I  do  not  make  this  proposition 
of  reform  here  for  the  first  time.  I  have  no  doubt,  moreover,  that  such  radical 
changes  will  only  be  slowly  introduced. 


ON  THE  CLASSICS  AND  THE  SCIENCES.         369 

discipline.  It  seems  also  unnecessary  that  all  branches 
should  be  treated  at  school,  and  that  exactly  the  same 
studies  should  be  pursued  in  all  schools.  A  single 
philological,  a  single  historical,  a  single  mathematical, 
a  single  scientific  branch,  pursued  as  common  subjects 
of  instruction  for  all  pupils,  are  sufficient  to  accom- 
plish all  that  is  necessary  for  the  intellectual  develop- 
ment. On  the  other  hand,  a  wholesome  mutual  stim- 
ulus would  be  produced  by  this  greater  variety  in  the 
positive  culture  of  men.  Uniforms  are  excellent  for 
soldiers,  but  they  will  not  fit  heads.  Charles  V.  learned 
this,  and  it  should  never  be  forgotten.  On  the  contrary, 
teachers  and  pupils  both  need  considerable  latitude,  if 
they  are  to  yield  good  results. 

With  John  Karl  Becker  I  am  of  the  opinion  that 
the  utility  and  amount  for  individuals  of  every  study 
should  be  precisely  determined.  All  that  exceeds  this 
amount  should  be  unconditionally  banished  from  the 
lower  classes.  With  respect  to  mathematics,  Becker,* 
in  my  judgment,  has  admirably  solved  this  question. 

With  respect  to  the  upper  classes  the  demand  as- 
sumes a  different  form.  Here  also  the  amount  of  mat- 
ter obligatory  on  all  pupils  ought  not  to  exceed  a  cer- 
tain limit.  But  in  the  great  mass  of  knowledge  that  a 
young  man  must  acquire  to-day  for  his  profession  it  is 
no  longer  just  that  ten  years  of  his  youth  should  be 
wasted  with  mere  preludes.  The  upper  classes  should 
supply  a  truly  useful  preparation  for  the  professions, 

*Die  Mathematik  alt  Lehrgtgenstand  dt*  Gym*asi*mi,  Berlin,  iWj. 


370         ON  THE  CLASSICS  AND  THE  SCIENCES. 

and  should  not  be  modelled  upon  the  wants  merely  of 
future  lawyers,  ministers,  and  philologists.  Again,  it 
would  be  both  foolish  and  impossible  to  attempt  to 
prepare  the  same  person  properly  for  all  the  different 
professions.  In  such  case  the  function  of  the  schools 
would  be,  as  Lichtenberg  feared,  simply  to  select  the 
persons  best  fitted  for  being  drilled,  whilst  precisely  the 
finest  special  talents,  which  do  not  submit  to  indis- 
criminate discipline,  would  be  excluded  from  the  con- 
test. Hence,  a  certain  amount  of  liberty  in  the  choice 
of  studies  must  be  introduced  in  the  upper  classes,  by 
means  of  which  it  will  be  free  for  every  one  who  is  clear 
about  the  choice  of  his  profession  to  devote  his  chief 
attention  either  to  the  study  of  the  philologico-histor- 
ical  or  to  that  of  the  mathematico- scientific  branches. 
Then  the  matter  now  treated  could  be  retained,  and  in 
some  branches,  perhaps,  judiciously  extended,*  without 
burdening  the  scholar  with  many  branches  or  increas- 
ing the  number  of  the  hours  of  study.  With  more 
homogeneous  work  the  student's  capacity  for  work  in- 
creases, one  part  of  his  labor  supporting  the  other 
instead  of  obstructing  it.  If,  however,  a  young  man 
should  subsequently  choose  a  different  profession,  then 
it  is  his  business  to  make  up  what  he  has  lost.  No 

*  Wrong  as  it  is  to  burden  future  physicians  and  scientists  with  Greek  for 
the  sake  of  the  theologians  and  philologists,  it  would  be  just  as  wrong  to  com- 
pel theologians  and  philologists,  on  account  of  the  physicians,  to  study  such 
subjects  as  analytical  geometry.  Moreover,  I  cannot  believe  that  ignorance 
of  analytical  geometry  would  be  a  serious  hindrance  to  a  physician  that  was 
otherwise  well  versed  in  quantitative  thought.  No  special  advantage  generally 
is  observable  in  the  graduates  of  the  Austrian  gymnasiums,  all  of  whom  have 
studied  analytical  geometry.  [Refers  to  an  assertion  of  Dubois-Reymond.] 


ON  THE  CLASSICS  AND   THE  SCIENCES.         371 

harm  certainly  will  come  to  society  from  this  change, 
nor  could  it  be  regarded  as  a  misfortune  if  philologists 
and  lawyers  with  mathematical  educations  or  physical 
scientists  with  classical  educations  should  now  and 

then  appear. 

* 
*  * 

The  view  is  now  wide-spread  that  a  Latin  and 
Greek  education  no  longer  meets  the  general  wants  of 
the  times,  that  a  more  opportune,  a  more  "liberal" 
education  exists.  The  phrase,  "a  liberal  education," 
has  been  greatly  misused.  A  truly  liberal  education  is 
unquestionably  very  rare.  The  schools  can  hardly  offer 
such ;  at  best  they  can  only  bring  home  to  the  student 
the  necessity  of  it.  It  is,  then,  his  business  to  acquire, 
as  best  he  can,  a  more  or  less  liberal  education.  It 
would  be  very  difficult,  too,  at  any  one  time  to  give  a 
definition  of  a  "  liberal "  education  which  would  satisfy 
every  one,  still  more  difficult  to  give  one  which  would 
hold  good  for  a  hundred  years.  The  educational 
ideal,  in  fact,  varies  much.  To  one,  a  knowledge  of 
classical  antiquity  appears  not  too  dearly  bought  "with 
early  death."  We  have  no  objection  to  this  person, 
or  to  those  who  think  like  him,  pursuing  their  ideal 
after  their  own  fashion.  But  we  may  certainly  protest 
strongly  against  the  realisation  of  such  ideals  on  our 
own  children.  Another,— Plato,  for  example,— puts 
men  ignorant  of  geometry  on  a  level  with  animals.* 

*  Compare  M.  Cantor,  Getchichte  der  Mathtmatik,  Leipsic,  1880,  Vol.  I,  p. 
193. 


372         ON  THE  CLASSICS  AND  THE  SCIENCES. 

If  such  narrow  views  had  the  magical  powers  of  the 
sorceress  Circe,  many  a  man  who  perhaps  justly 
thought  himself  well  educated  would  become  con- 
scious of  a  not  very  flattering  transformation  of  him- 
self. Let  us  seek,  therefore,  in  our  educational  sys- 
tem to  meet  the  wants  of  the  present,  and  not  estab- 
lish prejudices  for  the  future. 

But  how  does  it  come,  we  must  ask,  that  institu- 
tions so  antiquated  as  the  German  gymnasiums  could 
subsist  so  long  in  opposition  to  public  opinion?  The 
answer  is  simple.  The  schools  were  first  organised  by 
the  Church ;  since  the  Reformation  they  have  been  in 
the  hands  of  the  State.  On  so  large  a  scale,  the  plan 
presents  many  advantages.  Means  can  be  placed  at 
the  disposal  of  education  such  as  no  private  source,  at 
least  in  Europe,  could  furnish.  Work  can  be  con- 
ducted upon  the  same  plan  in  many  schools,  and  so 
experiments  made  of  extensive  scope  which  would  be 
otherwise  impossible.  A  single  man  with  influence 
and  ideas  can  under  such  circumstances  do  great 
things  for  the  promotion  of  education. 

But  the  matter  has  also  its  reverse  aspect.  The 
party  in  power  works  for  its  own  interests,  uses  the 
schools  for  its  special  purposes.  Educational  compe- 
tition is  excluded,  for  all  successful  attempts  at  im- 
provement are  impossible  unless  undertaken  or  per- 
mitted by  the  State.  By  the  uniformity  of  the  people's 
education,  a  prejudice  once  in  vogue  is  permanently 
established.  The  highest  intelligences,  the  strongest 


ON  THE  CLASSICS  AND  THE  SCIENCES.         373 

wills  cannot  overthrow  it  suddenly.  In  fact,  as  every- 
thing is  adapted  to  the  view  in  question,  a  sudden 
change  would  be  physically  impossible.  The  two 
classes  which  virtually  hold  the  reins  of  power  in  the 
State,  the  jurists  and  theologians,  know  only  the  one- 
sided, predominantly  classical  culture  which  they  have 
acquired  in  the  State  schools,  and  would  have  this  cul- 
ture alone  valued.  Others  accept  this  opinion  from 
credulity;  others,  underestimating  their  true  worth  for 
society,  bow  before  the  power  of  the  prevalent  opin- 
ion ;  others,  again,  affect  the  opinion  of  the  ruling 
classes  even  against  their  better  judgment,  so  as  to 
abide  on  the  same  plane  of  respect  with  the  latter.  I 
will  make  no  charges,  but  I  must  confess  that  the  de- 
portment of  medical  men  with  respect  to  the  question 
of  the  qualification  of  graduates  of  your  Realschulen 
has  frequently  made  that  impression  upon  me.  Let 
us  remember,  finally,  that  an  influential  statesman, 
even  within  the  boundaries  which  the  law  and  public 
opinion  set  him,  can  do  serious  harm  to  the  cause 
of  education  by  considering  his  own  one-sided  views 
infallible,  and  in  enforcing  them  recklessly  and  incon- 
siderately— which  not  only  can  happen,  but  has,  re- 
peatedly, happened.*  The  monopoly  of  education  by 
the  State  f  thus  assumes  in  our  eyes  a  somewhat  differ- 
ent aspect.  And  to  revert  to  the  question  above  asked, 
there  is  not  the  slightest  doubt  that  the  German  gym- 

*  Compare  Paulsen,  /.  c.,  pp.  607,  688. 

t  It  is  to  be  hoped  that  the  Americans  will  jealously  guard  their  schools 
and  universities  against  the  influence  of  the  State. 


374         ON  THE  CLASSICS  AND  THE  SCIENCES. 

nasiums  in  their  present  form  would  have  ceased  to 
exist  long  ago  if  the  State  had  not  supported  them. 

All  this  must  be  changed.  But  the  change  will 
not  be  made  of  itself,  nor  without  our  energetic  inter- 
ference, and  it  will  be  made  slowly.  But  the  path  is 
marked  out  for  us,  the  will  of  the  people  must  acquire 
and  exert  upon  our  school  legislation  a  greater  and 
more  powerful  influence.  Furthermore,  the  questions 
at  issue  must  be  publicly  and  candidly  discussed  that 
the  views  of  the  people  may  be  clarified.  All  who  feel 
the  insufficiency  of  the  existing  regime  must  combine 
into  a  powerful  organisation  that  their  views  may 
acquire  impressiveness  and  the  opinions  of  the  indi- 
vidual not  die  away  unheard. 

I  recently  read,  gentlemen,  in  an  excellent  book  of 
travels,  that  the  Chinese  speak  with  unwillingness  of 
politics.  Conversations  of  this  sort  are  usually  cut 
short  with  the  remark  that  they  may  bother  about  such 
things  whose  business  it  is  and  who  are  paid  for  it. 
Now  it  seems  to  me  that  it  is  not  only  the  business  of 
the  State,  but  a  very  serious  concern  of  all  of  us,  how 
our  children  shall  be  educated  in  the  public  schools 
at  our  cost. 


APPENDIX. 


A  CONTRIBUTION  TO  THE  HISTORY  OF  ACOUSTICS.* 

TT  THILE  searching  for  papers  by  Amontons,  sev- 
»  '  eral  volumes  of  the  Memoirs  of  the  Paris  Acad- 
emy for  the  first  years  of  the  eighteenth  century,  fell 
into  my  hands.  It  is  difficult  to  portray  the  delight 
which  one  experiences  in  running  over  the  leaves  of 
these  volumes.  One  sees  as  an  actual  spectator  almost 
the  rise  of  the  most  important  discoveries  and  wit- 
nesses the  progress  of  many  fields  of  knowledge  from 
almost  total  ignorance  to  relatively  perfect  clearness. 
I  propose  to  discuss  here  the  fundamental  re- 
searches of  Sauveur  in  Acoustics.  It  is  astonishing 
how  extraordinarily  near  Sauveur  was  to  the  view 
which  Helmholtz  was  the  first  to  adopt  in  its  full  ex- 
tent a  hundred  and  fifty  years  later. 

The  Histoire  de  I'Acadtmic  for  1700,  p.  131,  tells 
us  that  Sauveur  had  succeeded  in  making  music  an 

"This  article,  which  appeared  in  the  Proceedings  of  the  German  Mathe- 
matical Society  of  Prague  for  the  year  189*.  is  printed  as  a  supplement  to  the 
article  on  "The  Causes  of  Harmony,"  at  page  32. 


376  ON  THE  HIS  TOR  Y  OF  A  CO  US  TICS. 

object  of  scientific  research,  and  that  he  had  invested 
the  new  science  with  the  name  of  "acoustics."  On 
five  successive  pages  a  number  of  discoveries  are  re- 
corded which  are  more  fully  discussed  in  the  volume 
for  the  year  following. 

Sauveur  regards  the  simplicity  of  the  ratios  obtain- 
ing between  the  rates  of  vibration  of  consonances  as 
something  universally  known.*  He  is  in  hope,  by 
further  research,  of  determining  the  chief  rules  of  mu- 
sical composition  and  of  fathoming  the  "metaphysics 
of  the  agreeable,"  the  main  law  of  which  he  asserts 
to  be  the  union  of  "simplicity  with  multiplicity." 
Precisely  as  Eulerf  did  a  number  of  years  later,  he 
regards  a  consonance  as  more  perfect  according  as 
the  ratio  of  its  vibrational  rates  is  expressed  in  smaller 
whole  numbers,  because  the  smaller  these  whole  num- 
bers are  the  oftener  the  vibrations  of  the  two  tones 
coincide,  and  hence  the  more  readily  they  are  appre- 
hended. As  the  limit  of  consonance,  he  takes  the 
ratio  5:6,  although  he  does  not  conceal  the  fact  that 
practice,  sharpened  attention,  habit,  taste,  and  even 
prejudice  play  collateral  r61es  in  the  matter,  and  that 
consequently  the  question  is  not  a  purely  scientific 
one. 

Sauveur's  ideas  took  their  development  from  his 


*The  present  exposition  is  taken  from  the  volumes  for  1700  (published  in 
1703)  and  for  1701  (published  in  1704),  and  partly  also  from  the  Hittoire  dt 
I'Acadimie  and  partly  from  the  Mimoires.  Sauveur's  later  works  enter  less 
into  consideration  here. 

tKuler,  Ttntamen  nova*  theoriae  tnusicat.     Petropoli,  1739. 


ON  THE  HISTORY  OF  ACOUSTICS.  377 

having  instituted  at  all  points  more  exact  quantitative 
investigations  than  his  predecessors.  He  is  first  de- 
sirous of  determining  as  the  foundation  of  musical 
tuning  a  fixed  note  of  one  hundred  vibrations  which 
can  be  reproduced  at  any  time ;  the  fixing  of  the  notes 
of  musical  instruments  by  the  common  tuning  pipes 
then  in  use  with  rates  of  vibration  unknown,  appear- 
ing to  him  inadequate.  According  to  Mersenne  (Har- 
monic Universelle,  1636),  a  given  cord  seventeen  feet 
long  and  weighted  with  eight  pounds  executes  eight 
visible  vibrations  in  a  second.  By  diminishing  its 
length  then  in  a  given  proportion  we  obtain  a  propor- 
tionately augmented  rate  of  vibration.  But  this  pro- 
cedure appears  too  uncertain  to  Sauveur,  and  he  em- 
ploys for  his  purpose  the  beats  (battemens),  which  were 
known  to  the  organ-makers  of  his  day,  and  which  he 
correctly  explains  as  due  to  the  alternate  coincidence 
and  non-coincidence  of  the  same  vibrational  phases  of 
differently  pitched  notes.*  At  every  coincidence  there 
is  a  swelling  of  the  sound,  and  hence  the  number  of 
beats  per  second  will  be  equal  to  the  difference  of  the 
rates  of  vibration.  If  we  tune  two  of  three  organ-pipes 
to  the  remaining  one  in  the  ratio  of  the  minor  and  ma- 
jor third,  the  mutual  ratio  of  the  rates  of  vibration  of 
the  first  two  will  be  as  24:  25,  that  is  to  say,  for  every 
24  vibrations  to  the  lower  note  there  will  be  25  to  the 
higher,  and  one  beat.  If  the  two  pipes  give  together 

*In  attempting  to  perform  his  experiment  of  beats  before  the  Academy, 
Sauveur  was  not  quite  successful.     Histoire  dt  I'Acadtmit,  Anne>  1700,  p.  13*. 


3?8  ON  THE  HISTORY  OF  ACOUSTICS. 

four  beats  in  a  second,  then  the  higher  has  the  fixed 
tone  of  100  vibrations.  The  open  pipe  in  question 
will  consequently  be  five  feet  in  length.  We  also  de- 
termine by  this  procedure  the  absolute  rates  of  vibra- 
tion of  all  the  other  notes. 

It  follows  at  once  that  a  pipe  eight  times  as  long 
or  40  feet  in  length  will  yield  a  vibrational  rate  of 
12^,  which  Sauveur  ascribes  to  the  lowest  audible 
tone,  and  further  also  that  a  pipe  64  times  as  small 
will  execute  6,400  vibrations,  which  Sauveur  took  for 
the  highest  audible  limit.  The  author's  delight  at  his 
successful  enumeration  of  the  "imperceptible  vibra- 
tions" is  unmistakably  asserted  here,  and  it  is  justified 
when  we  reflect  that  to-day  even  Sauveur's  principle, 
slightly  modified,  constitutes  the  simplest  and  most 
delicate  means  we  have  for  exactly  determining  rates 
of  vibration.  Far  more  important  still,  however,  is  a 
second  observation  which  Sauveur  made  while  study- 
ing beats,  and  to  which  we  shall  revert  later. 

Strings  whose  lengths  can  be  altered  by  movable 
bridges  are  much  easier  to  handle  than  pipes  in  such 
investigations,  and  it  was  natural  that  Sauveur  should 
soon  resort  to  their  use. 

One  of  his  bridges  accidentally  not  having  been 
brought  into  full  and  hard  contact  with  the  string, 
and  consequently  only  imperfectly  impeding  the  vibra- 
tions, Sauveur  discovered  the  harmonic  overtones  of 
the  string,  at  first  by  the  unaided  ear,  and  concluded 
from  this  fact  that  the  string  was  divided  into  aliquot 


Off  THE  HISTORY  OF  ACOUSTICS.  379 

parts.  The  string  when  plucked,  and  when  the  bridge 
stood  at  the  third  division  for  example,  yielded  the 
twelfth  of  its  fundamental  note.  At  the  suggestion 
of  some  academician*  probably,  variously  colored 
paper  riders  were  placed  at  the  nodes  (noeuds)  and 
ventral  segments  (venires],  and  the  division  of  the 
string  due  to  the  excitation  of  the  overtones  (sons 
harmoniques)  belonging  to  its  fundamental  note  (son 
fondamcntal}  thus  rendered  visible.  For  the  clumsy 
bridge  the  more  convenient  feather  or  brush  was  soon 
substituted. 

While  engaged  in  these  investigations  Sauveur  also 
observed  the  sympathetic  vibration  of  a  string  induced 
by  the  excitation  of  a  second  one  in  unison  with  it. 
He  also  discovered  that  the  overtone  of  a  string  can 
respond  to  another  string  tuned  to  its  note.  He  even 
went  further  and  discovered  that  on  exciting  one  string 
the  overtone  which  it  has  in  common  with  another, 
differently  pitched  string  can  be  produced  on  that 
other  ;  for  example,  on  strings  having  for  their  vibra- 
tional  ratio  3:4,  the  fourth  of  the  lower  and  the  third 
of  the  higher  may  be  made  to  respond.  It  follows  in- 
disputably from  this  that  the  excited  string  yields 
overtones  simultaneously  with  its  fundamental  tone. 
Previously  to  this  Sauveur's  attention  had  been  drawn 
by  other  observers  to  the  fact  that  the  overtones  of 
musical  instruments  can  be  picked  out  by  attentive 
listening,  particularly  in  the  night. f  He  himself  men- 

+  ffistoirt  dt  fAcadlmit,  Ann(§e  1701,  p.  134-  t/W.,  P-  «9>- 


380  ON  THE  HISTORY  OF  ACOUSTICS. 

tions  the  simultaneous  sounding  of  the  overtones  and 
the  fundamental  tone.*  That  he  did  not  give  the 
proper  consideration  to  this  circumstance  was,  as  will 
afterwards  be  seen,  fatal  to  his  theory. 

While  studying  beats  Sauveur  makes  the  remark 
that  they  are  displeasing  to  the  ear.  He  held  the  beats 
were  distinctly  audible  only  when  less  than  six  oc- 
curred in  a  second.  Larger  numbers  were  not  dis- 
tinctly perceptible  and  gave  rise  accordingly  to  no 
disturbance.  He  then  attempts  to  reduce  the  differ- 
ence between  consonance  and  dissonance  to  a  ques- 
tion of  beats.  Let  us  hear  his  own  words,  f 

1 '  Beats  are  unpleasing  to  the  ear  because  of  the  unevenness 
of  the  sound,  and  it  may  be  held  with  much  plausibility  that  the 
reason  why  octaves  are  so  pleasing  is  that  we  never  hear  their 
beats.! 

"In  following  out  this  idea,  we  find  that  the  chords  whose 
beats  we  cannot  hear  are  precisely  those  which  the  musicians  call 
consonances  and  that  those  whose  beats  are  heard  are  the  disso- 
nances, and  that  when  a  chord  is  a  dissonance  in  one  octave  and  a 
consonance  in  another,  it  beats  in  the  one  and  does  not  beat  in  the 
other.  Consequently  it  is  called  an  imperfect  consonance.  It  is 
very  easy  by  the  principles  of  M.  Sauveur,  here  established,  to  as- 
certain what  chords  beat  and  in  what  octaves,  above  or  below  the 
fixed  note.  If  this  hypothesis  be  correct,  it  will  disclose  the  true 
source  of  the  rules  of  composition,  hitherto  unknown  to  science, 
and  given  over  almost  entirely  to  judgment  by  the  ear.  These 
sorts  of  natural  judgment,  marvellous  though  they  may  sometimes 

*Histoire  de  I'Acadtmie,  Anne~e  1702,  p.  91. 
tFrom  the  Histoire  de  I'Acadtmie,  Anne'e  1700,  p.  139. 
t  Because  all  octaves  in  use  in  music  offer  too  great  differences  of  rates 
of  vibration. 


ON  THE  HISTORY  OF  ACOUSTICS.  381 

appear,  are  not  so  but  have  very  real  causes,  the  knowledge  of 
which  belongs  to  science,  provided  it  can  gain  possession  thereof."* 

Sauveur  thus  correctly  discerns  in  beats  the  cause 
of  the  disturbance  of  consonance,  to  which  all  dishar- 
mony is  "probably"  to  be  referred.  It  will  be  seen, 
however,  that  according  to  his  view  all  distant  inter- 
vals must  necessarily  be  consonances  and  all  near  in- 
tervals dissonances.  He  also  overlooks  the  absolute 
difference  in  point  of  principle  between  his  old  view, 
mentioned  at  the  outset,  and  his  new  view,  rather  at- 
tempting to  obliterate  it. 

R.  Smithf  takes  note  of  the  theory  of  Sauveur  and 
calls  attention  to  the  first  of  the  above-mentioned  de- 
fects. Being  himself  essentially  involved  in  the  old 
view  of  Sauveur,  which  is  usually  attributed  to  Euler, 
he  yet  approaches  in  his  criticism  a  brief  step  nearer 


*  "  Les  battemens  ne  plaisent  pas  a  1'Oreille,  a  cause  de  I'in6galit6  du  son, 
et  Ton  peut  croire  avec  beaucoup  d'apparence  que  ce  qui  rend  les  Octaves  si 
agrdables,  c'est  qu'on  n'y  entend  jamais  de  battemens. 

"En  suivant  cette  ide'e,  on  trouve  que  les  accords  dont  on  ne  pent  entendre 
les  battemens,  sont  justement  ceux  que  les  Musiciens  traitent  de  Consonances, 
et  que  ceux  dont  les  battemens  se  font  sentir,  sont  les  Dissonances,  et  que 
quand  un  accord  est  Dissonance  dans  une  certaine  octave  et  Consonance 
dans  une  autre,  c'est  qu'il  bat  dans  1'une,  et  qu'il  ne  bat  pas  dans  1'autre. 
Aussi  est  il  traite'  de  Consonance  imparfaite.  II  est  fort  ais6  par  les  principes 
de  Mr.  Sauveur  qu'on  a  e'tablis  ici,  de  voir  quels  accords  battent,  et  dans 
quelles  Octaves  au-dessus  ou  au-dessous  du  son  fixe.  Si  cette  hypothese  est 
vraye,  elle  d<5couvrira  la  veritable  source  des  Regies  de  la  composition,  in- 
connue  jusqu'a  present  *  la  Philosophic,  qui  s'en  remettait  presque  entifcre- 
ment  au  jugement  de  1'Oreille.  Ces  sortes  de  jugemens  naturels,  quelque 
bisarres  qu'ils  paroissent  quelquefois,  ne  le  sont  point,  ils  ont  des  causes 
tres  nSelles,  dont  la  connaissance  appartient  a  la  Philosophic,  pourvue  qu'elU 
s'en  puisse  inettre  en  possession." 

t  Harmonics  or  the  Philosophy  of  Musical  So**ds,  Cambridge,  1749-  I  ««w 
this  book  only  hastily  in  1864  and  drew  attention  to  it  in  a  work  published  in 
1866.  I  did  not  come  into  its  actual  possession  until  three  years  ago  and  (hen 
only  did  I  learn  its  exact  contents. 


382  Otf  THE  HISTORY  OF  ACOUSTICS. 

to  the  modern  theory,  as  appears  from  the  following 
passage.* 

"The  truth  is,  this  gentleman  confounds  the  distinction  be- 
tween perfect  and  imperfect  consonances,  by  comparing  imperfect 
consonances  which  beat  because  the  succession  of  their  short  cy- 
clesf  is  periodically  confused  and  interrupted,  with  perfect  ones 
which  cannot  beat,  because  the  succession  of  their  short  cycles  is 
never  confused  nor  interrupted. 

' '  The  fluttering  roughness  above  mentioned  is  perceivable 
in  all  other  perfect  consonances,  in  a  smaller  degree  in  proportion 
as  their  cycles  are  shorter  and  simpler,  and  their  pitch  is  higher  ; 
and  is  of  a  different  kind  from  the  smoother  beats  and  undula- 
tions of  tempered  consonances  ;  because  we  can  alter  the  rate  of 
the  latter  by  altering  the  temperament,  but  not  of  the  former,  the 
consonance  being  perfect  at  a  given  pitch  :  And  because  a  judicious 
ear  can  often  hear,  at  the  same  time,  both  the  flutterings  and  the 
beats  of  a  tempered  consonance ;  sufficiently  distinct  from  each 
other. 

"For  nothing  gives  greater  offence  to  the  header,  though  ig- 
norant of  the  cause  of  it,  than  those  rapid,  piercing  beats  of  high 
and  loud  sounds,  which  make  imperfect  consonances  with  one  an- 
other. And  yet  a  few  slow  beats,  like  the  slow  undulations  of  a 
close  shake  now  and  then  introduced,  are  far  from  being  disagree- 
able." 

Smith  is  accordingly  clear  that  other  "rough- 
nesses" exist  besides  the  beats  which  Sauveur  con- 
sidered, and  if  the  investigations  had  been  continued 
on  the  basis  of  Sauveur's  idea,  these  additional  rough- 
would  have  turned  out  to  be  the  beats  of  the 


*Harmonics,  pp.  118  and  143. 

t "  Short  cycle  "  is  the  period  in  which  the  same  phases  of  the  two  co- 
operant  tones  are  repeated. 


ON  THE  HISTORY  OF  ACOUSTICS.  383 

overtones,    and   the   theory   thus   have   attained  the 
point  of  view  of  Helmholtz. 

Reviewing  the  differences  between  Sauveur's  and 
Helmholtz's  theories,  we  find  the  following : 

1.  The  theory  according  to  which  consonance  de- 
pends on  the  frequent  and  regular  coincidence  of  vi- 
brations and  their  ease  of  enumeration,  appears  from 
the  new  point  of  view  inadmissible.     The  simplicity 
of  the  ratios  obtaining  between  the  rates  of  vibration 
is  indeed  a  mathematical  characteristic  of  consonance 
as  well  as  a  physical  condition  thereof,  for  the  reason 
that  the  coincidence  of  the  overtones  as  also  their 
further  physical  and   physiological   consequences   is 
connected  with  this  fact.     But  no  physiological  or  psy- 
chological explanation  of  consonance  is  given  by  this 
fact,  for  the  simple  reason  that  in  the  acoustic  nerve- 
process  nothing  corresponding  to  the  periodicity  of 
the  sonant  stimulus  is  discoverable. 

2.  In  the  recognition  of  beats  as  a  disturbance  of 
consonance,  both  theories  agree.     Sauveur's  theory, 
however,  does  not  take  into  account   the  fact  that 
clangs,  or  musical  sounds  generally,  are  composite 
and  that  the  disturbance  in  the  consonances  of  distant 
intervals  principally  arise  from  the  beats  of  the  over- 
tones.   Furthermore,  Sauveur  was  wrong  in  asserting 
that  the  number  of  beats  must  be  less  than  six  in  a 
second  in  order  to  produce  disturbances.  Even  Smith 
knows  that  very  slow  beats  are  not  a  cause  of  disturb- 
ance, and  Helmholtz  found  a  much  higher  numbei 


384  ON  THE  HISTORY  OF  ACOUSTICS. 

(33)  for  the  maximum  of  disturbance.  Finally,  Sau- 
veur  did  not  consider  that  although  the  number  of 
beats  increases  with  the  recession  from  unison,  yet 
their  strength  is  diminished.  On  the  basis  of  the 
principle  of  specific  energies  and  of  the  laws  of  sym- 
pathetic vibration  the  new  theory  finds  that  two  at- 
mospheric motions  of  like  amplitude  but  different  pe- 
riods, a  sin  (rf)  and  asm  [(r-f/o)  (*+T)],  cannot  be 
communicated  with  the  same  amplitude  to  the  same 
nervous  end-organ.  On  the  contrary,  an  end-organ 
that  reacts  best  to  the  period  r  responds  more  weakly 
to  the  period  r-\-  p,  the  two  amplitudes  bearing  to  each 
other  the  proportion  a:  <pa.  Here  <p  decreases  when 
p  increases,  and  when  />  =  0  it  becomes  equal  to  1,  so 
that  only  the  portion  of  the  stimulus  (pa  is  subject  to 
beats,  and  the  portion  (1  —  9?) a  continues  smoothly 
onward  without  disturbance. 

If  there  is  any  moral  to  be  drawn  from  the  history 
of  this  theory,  it  is  that  considering  how  near  Sau- 
veur's  errors  were  to  the  truth,  it  behooves  us  to  ex- 
ercise some  caution  also  with  regard  to  the  new  the- 
ory. And  in  reality  there  seems  to  be  reason  for 
doing  so. 

The  fact  that  a  musician  will  never  confound  a 
more  perfectly  consonant  chord  on  a  poorly  tuned 
piano  with  a  less  perfectly  consonant  chord  on  a  well 
tuned  piano,  although  the  roughness  in  the  two  cases 
may  be  the  same,  is  sufficient  indication  that  the  de- 
gree of  roughness  is  not  the  only  characteristic  of  a 


ON  THE  HISTOR  Y  OF  A  CO  USTICS.  j85 

harmony.  As  the  musician  knows,  even  the  harmonic 
beauties  of  a  Beethoven  sonata  are  not  easily  effaced 
on  a  poorly  tuned  piano;  they  scarcely  suffer  more 
than  a  Raphael  drawing  executed  in  rough  unfinished 
strokes.  The  positive  physiologic o-psychological  charac- 
teristic which  distinguishes  one  harmony  from  another 
is  not  given  by  the  beats.  Nor  is  this  characteristic 
to  be  found  in  the  fact  that,  for  example,  in  sounding 
a  major  third  the  fifth  partial  tone  of  the  lower  note 
coincides  with  the  fourth  of  the  higher  note.  This 
characteristic  comes  into  consideration  only  for  the 
investigating  and  abstracting  reason.  If  we  should 
regard  it  also  as  characteristic  of  the  sensation,  we 
should  lapse  into  a  fundamental  error  which  would 
be  quite  analogous  to  that  cited  in  (1). 

The  positive  physiological  characteristics  of  the  in- 
tervals would  doubtless  be  speedily  revealed  if  it  were 
possible  to  conduct  aperiodic,  for  example  galvanic, 
stimuli  to  the  single  sound-sensing  organs,  in  which 
case  the  beats  would  be  totally  eliminated.  Unfortun- 
ately such  an  experiment  can  hardly  be  regarded  as 
practicable.  The  employment  of  acoustic  stimuli  of 
short  duration  and  consequently  also  free  from  beats, 
involves  the  additional  difficulty  of  a  pitch  not  pre- 
cisely determinable. 


386          ON  THE  THEORY  OF  SPATIAL  VISION. 


REMARKS  ON  THE  THEORY  OF  SPATIAL  VISION.* 

According  to  Herbart,  spatial  vision  rests  on  re- 
production-series. In  such  an  event,  of  course,  and 
if  the  supposition  is  correct,  the  magnitudes  of  the 
residua  with  which  the  percepts  or  representations 
are  coalesced  (the  helps  to  coalescence)  are  of  cardi- 
nal influence.  Furthermore,  since  the  coalescences 
must  first  be  fully  perfected  before  they  make  their 
appearance,  and  since  upon  their  appearance  the  in- 
hibitory ratios  are  brought  into  play,  ultimately,  then, 
if  we  leave  out  of  account  the  accidental  order  of  time 
in  which  the  percepts  are  given,  everything  in  spatial 
vision  depends  on  the  oppositions  and  affinities,  or, 
in  brief,  on  the  qualities  of  the  percepts,  which  enter 
into  series. 

Let  us  see  how  the  theory  stands  with  respect  to 
the  special  facts  involved. 

i.  If  intersecting  series  only,  running  anteriorly 
and  posteriorly,  are  requisite  for  the  production  of 
spatial  sensation,  why  are  not  analogues  of  them  found 
in  all  the  senses? 

a.  Why  do  we  measure  differently  colored  objects 

"This  article,  designed  to  illustrate  historically  that  on  Symmetry,  at 
page  89,  first  appeared  in  Fichte's  Ztitschrift  fttr  Philosophie,  for  1865, 


ON  THE  THEORY  OF  SPATIAL  VISION.          387 

and  variegated  objects  with  one  and  the  same  spatial 
measure?  How  do  we  recognise  differently  colored 
objects  as  the  same  in  size  ?  Where  do  we  get  our 
measure  of  space  from  and  what  is  it? 

3.  Why  is  it  that  differently  colored  figures  of  the 
same  form  reproduce  one  another  and  are  recognised 
as  the  same? 

Here  are  difficulties  enough.  Herbart  is  unable  to 
solve  them  by  his  theory.  The  unprejudiced  student 
sees  at  once  that  his  "inhibition  by  reason  of  form" 
and  "preference  by  reason  of  form"  are  absolutely 
impossible.  Think  of  Herbart's  example  of  the  red 
and  black  letters. 

The  "help  to  coalescence"  is  a  passport,  so  to 
speak,  made  out  to  the  name  and  person  of  the  per- 
cept. A  percept  which  is  coalesced  with  another  can- 
not reproduce  all  others  qualitatively  different  from  it 
for  the  simple  reason  that  the  latter  are  in  like  manner 
coalesced  with  one  another.  Two  qualitatively  differ- 
ent series  certainly  do  not  reproduce  themselves  be- 
cause they  present  the  same  order  of  degree  of  coales- 
cence. 

If  it  is  certain  'that  only  things  simultaneous  and 
things  which  are  alike  are  reproduced,  a  basic  prin- 
ciple of  Herbart's  psychology  which  even  the  most 
absolute  empiricists  will  not  deny,  nothing  remains 
but  to  modify  the  theory  of  spatial  perception  or  to 
invent  in  its  place  a  new  principle  in  the  manner  indi- 
cated, a  step  which  hardly  any  one  would  seriously 


388          ON  THE  THEORY  OF  SPATIAL  VISION. 

undertake.    The  new  principle  could  not  fail  to  throw 
all  psychology  into  the  most  dreadful  confusion. 

As  to  the  modification  which  is  needed  there  can 
be  hardly  any  doubt  as  to  how  in  the  face  of  the  facts 
and  conformably  to  Herbart's  own  principles  it  is  to 
be  carried  out.  If  two  differently  colored  figures  of 
equal  size  reproduce  each  other  and  are  recognised  as 
equal,  the  result  can  be  due  to  nothing  but  to  the  ex- 
istence in  both  series  of  presentations  of  a  presenta- 
tion or  percept  which  is  qualitatively  the  same.  The 
colors  are  different.  Consequently,  like  or  equal  per- 
cepts must  be  connected  with  the  colors  which  are 
yet  independent  of  the  colors.  We  have  not  to  look 
long  for  them,  for  they  are  the  like  effects  of  the  mus- 
cular feelings  of  the  eye  when  confronted  by  the  two 
figures.  We  might  say  we  reach  the  vision  of  space 
by  the  registering  of  light-sensations  in  a  schedule  of 
graduated  muscle-sensations.* 

A  few  considerations  will  show  the  likelihood  of 
the  r61e  of  the  muscle-sensations.  The  muscular  ap- 
paratus of  one  eye  is  unsymmetrical.  The  two  eyes 
together  form  a  system  which  is  vertical  in  symmetry. 
This  already  explains  much. 

i.  The  position  of  a  figure  influences  its  view.  Ac- 
cording to  the  position  in  which  objects  are  viewed 
different  muscle-sensations  come  into  play  and  the 
impression  is  altered.  To  recognise  inverted  letters 

•Cornp.  Cornelius,   Ueber  das  Sehen  ;  Wundt,   Theorie  der  Sinneswahr- 
nehmvng. 


ON  THE  THEORY  OF  SPATIAL  VISION.          389 

as  such  long  experience  is  required.  The  best  proof 
of  this  are  the  letters  d,  b,  p,  q,  which  are  represented 
by  the  same  figure  in  different  positions  and  yet  are 
always  distinguished  as  different.* 

».  It  will  not  escape  the  attentive  observer  that  for 
the  same  reasons  and  even  with  the  same  figure  and 
in  the  same  position  the  fixation  point  is  also  decisive. 
The  figure  seems  to  change  during  the  act  of  vision. 
For  example,  an  eight-pointed  star  constructed  by 
successively  joining  in  a  regular  octagon  the  first  cor- 
ner with  the  fourth,  the  fourth  with  the  seventh,  etc., 
skipping  in  every  case  two  corners,  assumes  alter- 
nately, according  to  where  we  suffer  the  centre  of  vi- 
sion to  rest,  a  predominantly  architectonic  or  a  freer 
and  more  open  character.  Vertical  and  horizontal 
lines  are  always  differently  apprehended  from  what 
oblique  lines  are. 

3.  The  reason  why  we  prefer  vertical  symmetry 
and  regard  it  as  something  special  in  its  kind,  whereas 
we  do  not  recognise 
horizontal  symmetry 
at  all  immediately,  is 
due  to  the  vertical 
symmetry  of  the  mus- 
cular apparatus  of  the  eye.  The  left-hand  side  a  of 
the  accompanying  vertically  symmetrical  figure  in- 
duces in  the  left  eye  the  same  muscular  feelings  as  the 

*Comp.  Mach,  Ueber  dot  Sehen  von  Lagen  und  Winktln.    Sitwn&t.  d<r 
Wiener  Akademit  1861. 


390          ON  THE  THEORY  OF  SPATIAL  VISION. 

right-hand  side  b  does  in  the  right  eye.  The  pleasing 
effect  of  symmetry  has  its  cause  primarily  in  the  repe- 
tition of  muscular  feelings.  That  a  repetition  actually 
occurs  here,  sometimes  sufficiently  marked  in  char- 
acter as  to  lead  to  the  confounding  of  objects,  is 
proved  apart  from  the  theory  by  the  fact  which  is 
familiar  to  every  one  quern  dii  oderunt  that  children 
frequently  reverse  figures  from  the  right  to  the  left, 
but  never  from  above  downwards  ;  for  example,  write 
«  instead  of  3  until  they  finally  come  to  notice  the 
slight  difference.  Figure  50  shows  how  pleasing  the 

repetition  of  muscular 
feelings  may  be.     As 
F»g-  59-  will  be  readily  under- 

stood, vertical  and  horizontal  lines  exhibit  relations 
similar  to  symmetrical  figures  which  are  immediately 
disturbed  when  oblique  positions  are  chosen  for  the 
lines.  Compare  what  Helmholtz  says  regarding  the 
repetition  and  coincidence  of  partial  tones. 

I  may  be  permitted  to  add  a  general  remark.  It 
is  a  quite  universal  phenomenon  in  psychology  that 
certain  qualitatively  quite  different  series  of  percepts 
mutually  awaken  and  reproduce  one  another  and  in  a 
certain  aspect  produce  the  appearance  of  sameness  or 
similarity.  We  say  of  such  series  that  they  are  of 
like  or  of  similar  form,  naming  their  abstracted  like- 
ness form. 

1.  Of  spatial  figures  we  have  already  spoken. 

2.  We  call  two  melodies  like  melodies  when  they 


ON  THE  THEORY  OF  SPATIAL  VISION.          391 

present  the  same  succession  of  pitch-ratios ; 
the  absolute  pitch  (or  key)  may  be  as  different 
as  can  be.  We  can  so  select  the  melodies  that 
not  even  two  partial  tones  of  the  notes  in  each 
are  common.  Yet  we  recognise  the  melodies 
as  alike.  And,  what  is  more,  we  notice  the 
form  of  the  melody  more  readily  and  recognise 
it  again  more  easily  than  the  key  (the  absolute 
pitch)  in  which  it  was  played. 
3.  We  recognise  in  two  different  melodies  the 
same  rhythm  no  matter  how  different  the  mel- 
odies may  be  otherwise.  We  know  and  recog- 
nise the  rhythm  more  easily  even  than  the  ab- 
solute duration  (the  tempo). 

These  examples  will  suffice.  In  all  these  and  in 
all  similar  cases  the  recognition  and  likeness  cannot 
depend  upon  the  qualities  of  the  percepts,  for  these 
are  different.  On  the  other  hand  recognition,  con- 
formably to  the  principles  of  psychology,  is  possible 
only  with  percepts  which  are  the  same  in  quality. 
Consequently  there  is  no  other  escape  than  to  imagine 
the  qualitatively  unlike  percepts  of  the  two  series  as 
necessarily  connected  with  other  percepts  which  are 
qualitatively  alike. 

Since  in  differently  colored  figures  of  like  form,  like 
muscular  feelings  are  necessarily  induced  if  the  figures 
are  recognised  as  alike,  so  there  must  necessarily  lie 
at  the  basis  of  all  forms  also,  and  we  might  even  say 
at  the  basis  of  all  abstractions,  percepts  of  a  peculiar 


392          ON  THE  THEORY  OF  SPATIAL  VISION. 

quality.  And  this  holds  true  for  space  and  form  as 
well  as  for  time,  rhythm,  pitch,  the  form  of  melodies, 
intensity,  etc.  But  whence  is  psychology  to  derive  all 
these  qualities?  Have  no  fear,  they  will  all  be  found, 
as  were  the  sensations  of  muscles  for  the  theory  of 
space.  The  organism  is  at  present  still  rich  enough 
to  meet  all  the  requirements  of  psychology  in  this  di- 
rection, and  it  is  even  time  to  give  serious  ear  to  the 
question  of  "corporeal  resonance  "  which  psychology 
so  loves  to  dwell  on. 

Different  psychical  qualities  appear  to  bear  a  very 
intimate  mutual  relation  to  one  another.  Special  re- 
search on  the  subject,  as  well  also  as  the  demonstra- 
tion that  this  remark  may  be  generally  employed  in 
physics,  will  follow  later.* 

•Cornp.  Mach,  Zur  Theorie  det  GehOrorgans.  Sitsungsber.  der  Wiener 
Akad.  1863.—  Utber  tint  ft  Ertcheinungen  der  fhysiolog.  Akustik.  Ibid. ,  1864 . 


INDEX. 


Absolute,  temperature,  162;  time,  204; 
forecasts,  have  no  signification  in 
science,  206. 

Abstract,  meaning  of  the  term,  240. 

Abstraction,  180,  200,  208,  231. 

Acceleration,  organ  for  forward,  299 
etseq. 

Accelerations,  204,  216,  footnote,  225- 
226,  253- 

Accident,  logical  and  historical,  in 
science,  160, 168,  170,  213 ;  in  inven- 
tions and  discoveries,  262  et  seq. 

Accord,  the  pure  triple,  46. 

Accumulators,  electrical,  125  et  seq.; 
132,  footnote. 

Acoustic  color,  36. 

Acoustics,  Sauveur  on,  375  et  seq. 

Action  and  reaction,  importance  of 
the  principle  of,  191. 

Adaptation,  inorganic  and  inorganic 
matter, 2iC,229;in  scientific  thought, 
214-235- 

^Esthetics,  computation  as  a  princi- 
ple of,  34 ;  researches  in,  89,  foot- 
note; repetition,  a  principle  of,  91. 

Africa,  186,  234,  237. 

Agreeable  effects,  due  to  repetition 
of  sensations,  92,  97  et  seq. 

Agriculture,  transition  to,  265. 

Air-gun,  135. 

Alcohol  and  water,  mixture  of  oil 
and,  in  Plateau's  experiments,  4. 

Algebra,  economy  of,  196. 

Alien  thoughts  in  science,  196. 

All,  the,  88. 

Amontons,  174,  346. 

Ampere,  the  word,  314. 

Ampere's  swimmer,  207. 


Analogies,  mechanical,  157,  160;  gen 

erally,  236-258. 
Analogy,  defined,  250. 
Analysis,  188. 
Analytical  geometry,  not  necessary 

to  physicians,  370,  footnote. 
Anatomic     structures,     transparent 

stereoscopic  views  of,  74. 
Anatomy,  character  of  research  in, 

255- 

Andrieu,  Jules,  49,  footnote. 
Animals,  the  psychical  activity  of, 

190,  231 ;  the  language  of,  238;  their 

capacity  for  experience,  266  et  seq. 
Animism,  186,  187,  243,  254. 
Anisotropic  optical  fields,  227. 
Apparatus  for  producing  movements 

of  rotation,  287  et  seq. 
Arabesque,  an  inverted,  95. 
Arabian  Nights,  219. 
Arago,  270. 
Aral,  the  Sea  of,  239. 
Archaeopteryx,  257. 
Archimedes,  4,  237. 
Arcimboldo,  Giuseppe,  36. 
Area,  principle  of  least  superficial, 

et  seq. 
Ares,  the  bellowing  of  the  wounded 

272. 

Aristotelians,  283. 
Aristotle,  348,  296. 
Art,  development  of,  28  et  seq. 
Artillery,  practical,  334-335- 
Artistic  value  of  scientific  descrip 

tions,  254, 
Arts,  practical,  108. 
Ascent,  heights  of,  143-151- 
Asia,  234. 


394 


INDEX. 


Assyrians,  the  art  of,  79. 

Astronomer,  measures  celestial  by 
terrestrial  distances,  136. 

Astronomy,  antecedent  to  psychol- 
ogy. 90;  rigidity  of  its  truths,  221. 

Atomic  theories,  104. 

Atoms,  207. 

Attention,  the  role  of,  in  sensuous 
perception,  35  et  seq. 

Attraction,  generally,  226;  of  liquid 
particles,  13-14 ;  in  electricity,  109 
et  seq. 

Aubert,  298. 

Audition.    See  Ear. 

Austrian  gymnasiums,  370  footnote. 

Axioms,  instinctive  knowledge,  190. 

Babbage,  on  the  economy  of  machin- 
ery, 196. 

Bach,  20. 

Backwards,  prophesying,  253. 

Bacon,  Lord,  48,  280. 

Baer,  C.  E.  von,  235. 

Balance,  electrical,  127,  footnote ; 
torsion,  109,  168. 

Balloon,  a  hydrogen,  199. 

Barbarism  and  civilisation,  335  et 
seq. 

Bass-clef,  101. 

Bass,  fundamental,  44. 

Beats,  40-45,  377  et  seq. 

Beautiful,  our  notions  of,  variable, 
99- 

Beauty,  objects  of,  in  nature,  91. 

Becker,  J.  K.,  364,  369. 

Beethoven,  39,  44. 

Beginnings  of  science,  189,  191. 

Belvedere  Gallery  at  Vienna,  36. 

Bernoulli,  Daniel,  on  the  conserva- 
tion of  living  force,  149  ;  on  the  vi- 
brations of  strings,  249. 

Bernoulli,  James,  on  the  centre  of 
oscillation,  149. 

Bernoulli,  John,  on  the  conservation 
of  living  force,  149 ;  on  the  princi- 
ple of  virtual  velocities,  151. 

Bible,  parallel  passages  from,  for 
language  study,  356. 

Binocular  vision,  66  et  seq. 

Black,  his  theory  of  caloric,  138,  162; 
on  quantity  of  heat,  166,  174;  on 


latent  heat,  167,  178  ;  researches  in 

heat  generally,  244. 
Blind  cat.  303. 
Bodies,  heavy,  seek  their  places,  224 

etseq.;  rotating,  285. 
Body,  a  mental  symbol  for  groups  of 

sensations,  200-203;  the  human,  our 

knowledge  of,  go. 
Boltzmann,  236. 
Booth,  Mr.,  77. 
Borelli,  217. 
Boulder,  a  granite,  233. 
Bow-wave  of  ships  and  moving  pro- 
jectiles, 323  et  seq. 
Boys,  317. 
Bradley,  273. 
Brahman,  the,  63. 
Brain,  localisation  of  functions  in, 

210. 
Breuer,  272,  282  et  seq.;  293,  298,  300 

301,  303,  306. 

Brewster,  his  stereoscope,  73. 
Bridge,  invention  of  the,  264,  268. 
British  Association,  108. 
Brooklyn  Bridge,  75,  footnote. 
Brown,  Crum,  293,  301. 
Building,    our    concepts    directions 

for,  253;  facts  the  result  of,  253; 

science  compared  to,  257. 
Building-stones,  metrical  units  are, 

253- 

Busch,  328. 
Business    of    a    merchant,    science 

compared  to  the,  16. 
Butterfly,  a,  22. 

Calculating  machines,  their  econom- 
ical character,  196. 

Caloric,  theory  of,  stood  in  the  way 
of  scientific  advancement,  138,  167. 

Calypso,  the  island  of,  351. 

Canterbury,  Archbishop  of,  39. 

Cantor,  M.,  361,  footnote. 

Capacity,  electrical,  116  et  seq.,  123; 
thermal,  123 ;  specific  inductive 
117. 

Capulets  and  Montagues,  87. 

Cards,  difficult  games  of,  357. 

Carnot,  S.,  excludes  perpetual  mo 
tion  in  heat,  156,  162;  his  mechani 
cal  view  of  physics,  156;  on  thermo 


INDEX. 


395 


dynamics,  160  et  seq.;  his  principle, 

162;  also,  191. 

Carus,  Dr.  Paul,  265,  footnote. 
Casselli's  telegraph,  26. 
Cassini,  51. 
Cauchy,  character  of  the  intellectual 

activity  of  a,  195. 
Causal  insight,  awakened  by  science, 

357- 
Causality,  157-159, 190, 198  et  seq.,  221 

et  seq.,  237,  253,  254. 
Cause  and  effect,  198  et  seq.  See  also 

Causality. 
Centimetre-gramme-second  system, 

in. 
Centre  of  gravity,  must  lie  as  low  as 

possible  for  equilibrium  to  subsist, 

15 ;  Torricelli's  principle  of,  150  et 

seq. 

Centre  of  oscillation,  149. 
Change,  method  of,  in  science,  230. 
Changeable  character  of  bodies,  202. 
Changes,  physical,  how  they  occur, 
•  205. 

Character,  a  Universal  Real,  192. 
Character,  like  the  forms  of  liquids, 

3  ;  persons  of,  24. 
Charles  the  Fifth,  369. 
Chemical,  elements,    202;    symbols, 

192;  current,  118. 
Chemistry,  character  of  research  in, 

255 ;  the  method  of  thermodynam- 
ics in,  257. 
Child,  a,  modes  of  thought  of,  223; 

looking  into  a  moat,  208. 
Child  of  the  forest,  his  interpretation 

of  new  events,  218-219. 
Childish  questions,  199-200. 
Children,  the  drawings  of,  201-202. 
Chinese  language,  economy  of,  192, 

study  of,  354. 

Chinese  philosopher,  an  old,  186. 
Chinese,   speak  with   unwillingness 

of  politics,  374  ;  the  art  of,  79-80. 
Chosen,  many  are  called  but  few  are, 

65- 

Christ,  saying  of,  65. 
Christianity,  Latin  introduced  with, 

3". 
Christians  and  Jews,  monotheism  of 

the,  187. 


Church  and  State,  88. 

Cicero,  318. 

Circe,  372. 

Circle,  the  figure  of  least  area  with 

given  periphery,  12. 
Circular  polarisation,  242. 
Civilisation    and    barbarism,  335  et 

seq. 
Civilisation,  some  phenomena  of,  ex 

plained  by  binocular  vision,  74. 
Civilised  man,  his  modes  of  concep- 
tion and  interpretation,  219. 
Clapeyron,  162. 

Class-characters  of  animals,  255. 
Classical,  culture,  the  good  and  bad 

effects  of,  347;  scholars,  not  the  only 

educated  people,  345. 
Classics,  on  instruction  in,  338-374; 

the  scientific,  368. 
Classification  in  science,  255. 
Clausius,  on  thermodynamics,   165 ; 

on  reversible  cycles,  176. 
Claviatur,  Mach's,  42-43. 
Club-law,  335. 
Cochlea.the.a  species  of  piano-forte 

19- 

Cockchafer,  86. 

Coefficient  of  self-induction,  250,  252 
Colophonium,  solution  of,  7. 
Color,  acoustic,  36. 
Color-sensation,  210. 
Color-signs,  their  economy,  192. 
Colors,  origin  of  the  names  of,  239. 
Column,  body  moving  behind  a.  202 
Communication.itsfunctions.import 

and  fruits,  197,  238  et  seq.;  by  lan- 
guage, 237;  high  importance  of,  191 

et  seq. 

Comparative  physics,  239. 
Comparison  in  science,  231, 238  et  seq 
Computation,  a  principle  of  scsthet 

ics,  34- 
Concepts,  abstract,  defined,  250-252; 

metrical,  in  electricity,  107  et  seq 
Conceptual,  meaning  of  the  term, 240 
Conceptual  thought,  192. 
Concha,  18. 
Condensers,  electrical,  125  et  seq. 

132,  footnote. 
Conductors  and  non-conductors.  See 

Electrical,  etc. 


396 


INDEX. 


Conformity  in  the  deportment  of  the 
energies,  171-175. 

Confusion  of  objects,  cause  of,  95. 

Conic  sections,  257. 

Conical  refraction,  29,  242. 

Conservation  of  energy,  137  et  seq. 
See  Energy, 

Conservation  of  weight  or  mass,  203. 

Consonance,  connexion  of  the  simple 
natural  numbers  with,  33 ;  Euclid's 
definition  of,  33 ;  explanation  of, 
42 ;  scientific  definition  of,  44  ;  and 
dissonance  reduced  to  beats,  376, 
370,  383. 

Consonant  intervals,  43. 

Constancy  of  matter,  203. 

Constant,  the  dielectric,  117. 

Constants,  the  natural,  193. 

Continuum  of  facts,  256  et  seq. 

Cornelius,  388  footnote. 

Corti,  the  Marchese,  his  discovery  of 
minute  rods  in  the  labyrinth  of  the 
ear,  19. 

Coulomb,  his  electrical  researches, 
108,  109,  113  ;  his  notion  of  quantity 
of  electricity,  173 ;  his  torsion-bal- 
ance, 168. 

Crew,  Prof.  Henry,  317  footnote. 

Criticism,  Socrates  the  father  of  sci- 
entific, i,  16. 

Critique  of  Pure  Reason,  Kant' s,  188. 

Crucible,  derivation  of  the  word,  49, 
footnote. 

Crustacea,  auditory  filaments  of,  29, 
272,  302. 

Cube  of  oil,  5. 

Culture,  ancient  and  modern,  344. 

Currents,  chemical,  118;  electrical, 
118;  galvanic,  132;  measurement  of 
electrical,  135-136;  of  heat,  244,  249- 
250;  strength  of,  250. 

Curtius,  356. 

Curved  lines,  their  asymmetry,  98. 

Curves,  how  their  laws  are  investi- 
gated, 206. 

Cycles,  reversible,  Clausius  on,  176. 

Cyclical  processes,  closed,  175. 

Cyclops,  67. 

Cyclostat,  298. 

Cylinder,  of  oil,  6;  mass  of  gas  en- 
closed in  a,  179. 


D'Alembert,  on  the  causes  of  har- 
mony, 34  ;  his  principle,  142,  149, 
154  ;  also  234,  279- 

Danish  schools,  338,  footnote. 

Darwin,  his  study  of  organic  nature, 
215  et  seq. ;  his  methods  of  research, 
216. 

Deaf  and  dumb,  not  subject  to  giddi- 
ness, 299. 

Deaf  person,  with  a  piano,  analyses 
sounds,  27. 

Death  and  life,  186. 

Definition,  compendious,  197. 

Deiters,  19. 

Delage,  298,  301,  302. 

Democritus,  his  mechanical  concep- 
tion of  the  world,  155,  187. 

Demonstration,  character  of,  362. 

Deportment  of  the  energies,  con- 
formity in  the,  171-175. 

Derivation,  laws  only  methods  of, 
256. 

Descent,  Galileo's  laws  of,  193;  gen- 
erally, 143  et  seq.,  204,  215. 

Description,  108,  191,  236,  237  ;  a  con- 
dition of  scientific  knowledge,  193; 
direct  and  indirect,  240 ;  in  phys- 
ics, 197,  199. 

Descriptive  sciences,  their  resem- 
blance to  the  abstract,  248. 

Determinants,  195. 

Diderot,  234. 

Dielectric  constant,  the,  117. 

Difference-engine,  the,  196. 

Differential  coefficients,  their  rela- 
tion to  symmetry,  98. 

Differential  laws,  204. 

Differential  method,  for  detecting 
optical  imperfections,  317. 

Diffraction,  91,  194. 

Diffusion,  Pick's  theory  of,  249. 

Discharge  of  Leyden  jars,  114  et  seq 

Discoveries,  the  gist  of,  270,  375. 

Discovery  and  invention,  distinction 
between,  269. 

Dissonance,  explanation  of,  42;  defi 
nition  of,  33,  44.  See  Consonance. 

Distances,  estimation  of,  by  the  eye 
63  et  seq. 

Dogs,  like  tuning-forks,  23 ;  their 
mentality,  190. 


INDEX. 


397 


Domenech,  Abbe1,  92. 

Dramatic  element  in  science,  243. 

Drop  of  water,  on  a  greased  plate,  8; 
on  the  end  of  a  stick,  8 ;  in  free  de- 
scent, 8.  . 

Dubois,  218. 

Dubois-Reymond,  370,  footnote. 

Dufay,  271. 

Dynamics,  foundations  of,  153  et  seq. 

Ear,  researches  in  the  theory  of,  17 
et  seq.;  diagram  of,  18;  its  analysis 
of  sounds,  20  et  seq.;  a  puzzle-lock, 
28 ;  reflected  in  a  mirror,  93 ;  no 
symmetry  in  its  sensation,  103. 

Earth,  its  oblateness  not  due  to  its 
original  fluid  condition,  2;  rotation 
of,  204 ;  internal  disturbances  of, 
285. 

Economical,  nature  of  physical  in- 
quiry, 186  ;  procedure  of  the  human 
mind,  186 ;  order  fo  physics,  197; 
schematism  of  science,  206 ;  tools 
of  science,  207;  coefficient  of  dyna- 
mos, 133. 

Economy,  of  the  actions  of  nature,  15; 
the  purpose  of  science,  16 ;  of  lan- 
guage, 191  et  seq.;  of  the  industrial 
arts,  192;  of  mathematics,  195-196; 
of  machinery,  196;  of  self-preser- 
vation, our  first  knowledge  derived 
from,  197;  generally,  186  et  seq.,  269. 

Education,  higher,  86  ;  liberal,  341  et 
seq.,  371- 

Efflux,  liquid,  150. 

Ego,  its  nature,  234-235. 

Egypt,  234. 

Egyptians,  art  of,  78  et  seq.,  201. 

Eighteenth  century,  the  scientific 
achievements  of,  187,  188. 

Eleatics,  on  motion,  158. 

Electrical,  attraction  and  repulsion, 
109  et  seq.,  168;  capacity,  116  et  seq., 
force,  no,  119,  168;  spark,  117,  127, 
132,  133.  19°;  energy,  measurement 
of,  128  et  seq.,  169;  currents,  con- 
ceptions of,  118,  132,  135-136,  226- 
227,  249,  250;  fluids,  112  et  seq. ,228  ; 
pendulums,  no;  levels,  173;  po- 
tential, 121  et  seq. ;  quantity,  in, 
118,  119. 


Electricity,  as  a  substance  and  as  a 
motion,  170;  difference  between  the 
conceptions  of  heat  and,  168  et  seq., 
rflleof  work  in, 120  et  seq.;  galvanic, 
134-  See  Electrical. 

Electrometer,  W.  Thomson's  abso- 
lute, 127,  footnote. 

Electrometers,  122,  127. 

Electrostatic  unit,  in. 

Electrostatics,  concepts  of,  107  et 
seq. 

Elements,  interdependence  of  the 
sensuous,  179;  of  bodies,  202;  of 
phenomena,  equations  between, 
205;  of  sensations,  200;  used  in- 
stead of  sensations,  208-209. 

Ellipse,  equation  of,  205;  the  word, 
342- 

Embryology,  possible  future  state  of, 
257- 

Energies,  conformity  in  the  deport- 
ment of,  171-175 ;  differences  of, 
175- 

Energy,  a  metrical  notion,  178;  con- 
servation of,  137  et  seq. ;  defined, 
139;  metaphysical  establishment  of 
the  doctrine  of,  183;  kinetic,  177; 
potential,  128  et  seq.;  substantial 
conception  of,  164,  185,  244  et  seq.; 
conservation  of,  in  electrical  phe- 
nomena, 131  et  seq.;  limits  of  prin- 
ciple of,  175;  principle  of,  in  phys- 
ics, 160-166 ;  sources  of  principle 
of,  179,  181 ;  thermal,  177 ;  Thomas 
Young  on,  173. 

Energy-value  of  heat,  178,  footnote 

Enlightenment,  the,  188. 

Entropy,  a  metrical  notion,  178. 

Environment,  stability  of  our,  206. 

Equations  for  obtaining  facts,  180; 
between  the  elements  of  phenom- 
ena, 205. 

Equilibrium,  conditions  of,  in  simple 
machines,  151  ;  figures  of  liquid,  4 
etseq.;  general  condition  of,  15; 
in  the  State,  15. 

Etymology,  the  word,  misused  for  en- 
tomology, 316. 

Euclid,  on  consonance  and  disso- 
nance, 33  ;  his  geometry,  364. 

Euler,  on  the  causes  of  harmony,  34 ; 


398 


INDEX. 


impression  of  the  mathematical 
processes  on,  196 ;  on  the  vibrations 
of  strings,  249,  285,  376. 

Euler  and  Hermann's  principle,  149. 

Euthyphron,  questioned  by  Socra- 
tes, i. 

Evolute,  the  word,  342. 

Evolution,  theory  of,  as  applied  to 
ideas,  216  et  seq. 

Ewald,  298,  304. 

Excluded  perpetual  motion,  logical 
root  of  the  principle  of,  182. 

Exner,  S.,  302,  305. 

Experience,  communication  of,  191 ; 
our  ready,  199 ;  the  principle  of  en- 
ergy derived  from,  179 ;  the  well- 
spring  of  all  knowledge  of  nature, 
181 ;  incongruence  between  thought 
and,  206. 

Experimental  research,  function  of, 
181. 

Explanation,  nature  of,  194,  237,  362. 

Eye,  cannot  analyse  colors,  20 ;  re- 
searches in  the  theory  of  the,  18  et 
seq.;  loss  of,  as  affecting  vision,  98. 

Eyes,  purpose  of,  66  et  seq.;  their 
structure  symmetrical  not  identi- 
cal, 96. 


Face,  human,  inverted,  95. 

Facts  and  ideas, necessary  to  science, 
231. 

Facts,  description  of,  108  ;  agreement 
of,  180;  relations  of,  180;  how  rep- 
resented, 206;  reflected  in  imagina- 
tion, 220  et  seq.;  the  result  of  con- 
structions, 253 ;  a  continuum  of,  256 
et  seq.;  equations  for  obtaining, 
180. 

Falling  bodies,  204,  2:5 ;  Galileo  on 
the  law  of,  143  et  seq.,  284. 

Falling,  cats,  303,  footnote. 

Falstaff,  309. 

Familiar    intermediate    links    of 
thought,  198. 

Faraday,  191,  217,  237;  his  conception 
of  electricity,  114,  271. 

Fechner,  theory  of  Corti's  fibres,  19 
et  seq. 

Feeling,  cannot  be  explained  by  mo- 
tions of  atoms,  208  et  seq. 


Fetishism,  186,  243,  254  ;  in  our  phys 

ical  concepts,  187. 
Fibres  of  Corti,  17  et  seq. 
Fick,  his  theory  of  diffusion,  249. 
Figures,  symmetry  of,  92  et  seq. 
Figures  of  liquid  equilibrium^  et  seq 
Fire,  use  of,  264. 
Fishes,  306. 

Fixed  note,  determining  of  a,  377- 
Fizeau,  his  determination  of  the  ve 

locity  of  light,  55  et  seq. 
Flats,  reversed  into  sharps,  101. 
Flouren's  experiments,  272,  290. 
Flower-girl,  the  baskets  of  a,  95. 
Fluids,  electrical,  112  et  seq. 
Force,  electric,  no,  119,  168  ;  unit  of 

in  ;  living,  137,  149,  184  ;  generally 

253.    See  the  related  headings. 
Forces,  will  compared  to,  254. 
Foreseeing  events,  220  et  seq. 
Formal  conceptions,  r61e  of,  183. 
Formal  need  of  a  clear  view  of  facts 

183,  246 ;  how  far  it  corresponds  to 

nature,  184. 

Formative  forces  of  liquids,  4. 
Forms  of  liquids,  3  et  seq. 
Forward  movement,  sensation  of,  300. 
Forwards,  prophesying,  253. 
Foucault,  57,  70,  296. 
Foucault  and  Toepler,  method  of,  for 

detecting  optical  faults,  313  et  seq. 

320. 
Foundation    of    scientific     thought 

primitive  acts  of  knowledge  the 

190. 

Fourier,  on  processes  of  heat,  249,278. 
Fox,  a,  234. 
Franklin's  pane,  116. 
Frary,  338,  footnote. 
Fraunhofer,  271. 
Freezing-point,  lowered  by  pressure, 

162. 

Fresnel,  271. 
Fritsch,  321. 

Frogs,  larva?  of,  not  subject  to  ver- 
tigo, 298. 
Froude,  333. 

Frustra,  misuse  of  the  word,  345. 
Future,  science  of  the,  213. 

Galileo,1  on  the  motion  of  pendulums 


INDEX. 


399 


at ;  his  attempted  measurement  of 
the  velocity  of  light.  50  et  seq.;  his 
exclusion  of  a  perpetual  motion, 
143 ;  on  velocities  acquired  in  free 
descent,  143-147;  on  the  law  of  in- 
ertia, 146-147;  on  virtual  velocities, 
150;  on  work,  172;  his  laws  of  de- 
scent, 193 ;  on  falling  bodies,  225 ; 
great  results  of  his  study  of  nature, 
214  et  seq.;  his  rude  scientific  im- 
plements, 215 ;  selections  from  his 
works  for  use  in  instruction,  368; 
also  105,  182,  187,  237,  272,  274,  283. 

Galle,  observes  the  planet  Neptune, 
29. 

Galvanic,  electricity,  134;  current, 
132;  dizziness,  291 ;  vertigo,  298. 

Galvanoscope,  135. 

Galvanotropism,  291. 

Garda,  Lake,  239. 

Gas,  the  word,  264;  mass  of,  enclosed 
in  a  cylinder,  179. 

Gases,  tensions  of,  for  scales  of  tem- 
perature, 174. 

Gauss,  on  the  foundations  of  dynam- 
ics, 154;  his  principle,  154;  also, 
108,  274. 

Genius,  279,  280. 

Geography,  comparison  in,  239. 

Geometers,  in  our  eyes,  72. 

Geotropism,  289. 

German  schools  and  gymnasiums, 
372,  373.  338,  footnote. 

Ghosts,  photographic,  73. 

Glass,  invisible  in  a  mixture  of  the 
same  refrangibility,  312;  powdered, 
visible  in  a  mixture  of  the  same 
refrangibility,  312. 

Glove,  in  a  mirror,  93. 

Goethe,  quotations  from,  9,  31,  49,  88; 
on  the  cause  of  harmony,  35. 

Goltz,  282,  291. 

Gossot,  332. 

Gothic  cathedral,  94. 

Gravitation,  discovery  of,  225  et  seq. 

Gravity,  how  to  get  rid  of  the  effects 
of,  in  liquids,  4 ;  also  228. 

Gray,  Elisha,  his  telautograph,  26. 

Greased  plate,  drop  of  water  on  a,  8. 

Great  minds,  idiosyncrasies  of,  247. 

Greek  language,  scientific  terms  de- 


rived from,  342-343;  common  words 
derived  from,  343,  footnote ;  still 
necessary  for  some  professions, 
346 ;  its  literary  wealth,  347-348; 
narrowness  and  one-sidedness  of 
its  literature,  348-349 ;  its  excessive 
study  useless,  349-350;  its  study 
sharpens  the  judgment,  357-358 ;  a 
knowledge  of  it  not  necessary  to  a 
liberal  education,  371. 

Greeks,  their  provinciality  and  nar- 
row-mindedness, 349 ;  now  only  ob- 
jects of  historical  research,  350. 

Griesinger,  184. 

Grimaldi,  270. 

Grimm,  344,  footnote. 

Grunting  fishes,  306. 

Habitudes  of  thought,  199,  224,  227 
232. 

Haeckel,  222,  235. 

Hamilton,  deduction  of  the  conical 
refraction  of  light,  29. 

Hankel,  364. 

Harmonics,  38,  40. 

Harmony,  on  the  causes  of,  33  et 
seq.;  laws  of  the  theory  of,  ex- 
plained, 30;  the  investigation  of 
the  ancients  concerning,  32;  gen- 
erally, 103.  See  Consonance. 

Harris,  electrical  balance  of,  127, 
footnote. 

Hartwich,  Judge,  343,  353,  footnote. 

Hat,  a  high  silk,  24. 

Hats,  ladies',  development  of,  64. 

Head-wave  of  a  projectile,  323  et  seq 

Hearing  and  orientation,  relation 
between,  304  et  seq. 

Heat,  a  material  substance,  177;  dif- 
ference between  the  conceptions 
of  electricity  and,  168  et  seq.;  sub- 
stantial conception  of,  243  et  seq.; 
Carnot  on,  156,  160  et  seq.;  Fourier 
on  the  conduction  of,  249;  not  ne- 
cessarily a  motion,  167,  170,  171; 
mechanical  equivalent  of.  164,  167; 
of  liquefaction,  178;  quantity  of, 
166;  latent,  167,  178.  «44 :  specific. 
166,  244 ;  the  conceptions  of,  160- 
171;  machine,  160;  a  measure  of 
electrical  energy,  133  et  teq.;  me- 


4oo 


INDEX. 


chanical  theory  of,  133 ;  where  does 
it  come  from?  zoo. 

Heavy  bodies,  sinking  of,  222. 

Heights  of  ascent,  143-151. 

Helm,  172. 

Helmholtz,  applies  the  principle  of 
energy  to  electricity,  184;  his  tele- 
stereoscope,  84  ;  his  theory  of  Cor- 
ti's  fibres,  19  et  seq.;  on  harmony, 
35.  99 ;  on  the  conservation  of  en- 
ergy,i65,247;  his  method  of  thought, 
247 ;  also  138,  305,  307,  375,  383. 

Hensen,  V.,  on  the  auditory  function 
of  the  filaments  of  Crustacea,  29, 
302. 

Herbart,  386  et  seq. 

Herbartians,  on  motion,  158. 

Herculaneum,  art  in,  80. 

Heredity,  in  organic  and  inorganic 
matter,  216,  footnote. 

Hering,  on  development,  222 ;  on  vis- 
ion, 210. 

Hermann,  E.,  on  the  economy  of  the 
industrial  arts,  192. 

Hermann,  L.,  291. 

Herodotus,  26,  234,  347,  350. 

Hertz,  his  waves,  242  ;  his  use  of  the 
phrase  "prophesy,"  253. 

Herzen,  361,  footnote. 

Hindu  mathematicians,  their  beauti- 
ful problems,  30. 

Holtz's  electric  machine,  132. 

Horse,  63. 

Household,  physics  compared  to  a 
well-kept,  197. 

Housekeeping  in  science  and  civil 
life,  198. 

Hudson,  the,  94. 

Human  beings,  puzzle-locks,  27. 

Human  body,  our  knowledge  of,  90. 

Human  mind,  must  proceed  econom- 
ically, 186. 

Humanity,  likened  to  a  polyp-plant, 
235- 

Huygens,  his  mechanical  view  of 
physics,  155  ;  on  the  nature  of  light 
and  heat,  155-156;  his  principle  of 
the  heights  of  ascent,  149 ;  on  the 
law  of  inertia  and  the  motion  of  a 
compound  pendulum,  147-149;  on 
the  impossible  perpetual  motion, 


147-148;  on  work,  173;  selections 
from  his  works  for  use  in  instruc- 
tion, 368;  his  view  of  light,  227-228, 
262. 

Huygens,  optical  method  for  detect- 
ing imperfections  in  optical  glasses 
313- 

Hydrogen  balloon,  199. 

Hydrostatics,     Stevinus's    principle 

Qof,  141. 

Hypotheses.their  rdle  in  explanation, 
228  et  seq. 

Ichthyornis,  257. 

Ichthyosaurus,  63. 

Idea?  what  is  a  theoretical,  241. 

Idealism,  209. 

Ideas,  a  product  of  organic  nature, 
217  et  seq.;  and  facts,  necessary  to 
science,  231;  not  all  of  life,  233; 
their  growth  and  importance,  233 ; 
a  product  of  universal  evolution, 
235;  the  history  of,  227  et  seq.;  in 
great  minds,  228 ;  the  rich  contents 
of,  197;  their  unsettled  character 
in  common  life,  their  clarification 
in  science,  1-2. 

Ideography,  the  Chinese,  192. 

Imagery,  mental,  253. 

Imagination,  facts  reflected  in,  220 
et  seq. 

Inclined  plane,  law  of,  140-141. 

Incomprehensible,  the,  186. 

Indian,  his  modes  of  conception  and 
interpretation,  218  et  seq. 

Individual,  a  thread  on  which  pearls 
are  strung,  234-235- 

Industrial  arts,  economy  of  the,  E. 
Hermann  on,  192. 

Inertia,  law  of,  143  et  seq.,  146  et  seq.; 
216,  footnote,  283  et  seq. 

Innate  concepts  of  the  understand- 
ing, Kant  on,  199. 

Innervation,  visual,  99. 

Inquirer,  his  division  of  labor,  105 ; 
compared  to  a  shoemaker,  105-106; 
what  constitutes  the  great,  191 ;  the 
true,  seeks  the  truth  everywhere,  63 
et  seq.;  the, compared  to  a  wooer,45. 

Instinctive  knowledge,  189,  190. 

Instruction,  aim  of,  the  saving  of  ex- 


INDEX. 


401 


perience,  191;  in  the  classics,  math- 
ematics, anil  sciences,  338-374 ;  lim- 
itation of  matter  of,  365  et  seq. 

Insulators,  130. 

Integrals,  195. 

Intellectual  development,  conditions 
of,  286  et  seq. 

Intentions,  acts  of  nature  compared 
to,  14-15. 

Interconnexion  of  nature,  182. 

Interdependence,  of  properties,  361 ; 
of  the  sensuous  elements  of  the 
world,  179. 

Interference  experiments  with  the 
head-wave  of  moving  projectiles, 
327-328. 

International  intercourse, established 
by  Latin,  341. 

International  measures,  108. 

Invention,  discovery  and,  distinction 
between,  269. 

Inventions,  requisites  for  the  devel- 
opment of,  266,  268  et  seq. 

Iron-filings,  220,  243. 

Italian  art,  234. 

Jacobi,  C.  G.  J.,  on  mathematics,  280. 

James,  W.,  275,  299. 

Java,  163. 

Jews  and  Christians,  monotheism  of 
the,  187. 

Jolly,  Professor  von,  112,  474. 

Joule,  J.  P.,  on  the  conservation  of 
energy,  163-165,  167,  183 ;  his  con- 
ception of  energy,  245  ;  his  meta- 
physics, 183,  246;  his  method  of 
thought,  247  ;  also  137,  138. 

Journde,  317. 

Judge,  criminal,  the  natural  philoso- 
pher compared  to  a,  48. 

Judgment,  essentially  economy  of 
thought,  201-202;  sharpened  by  lan- 
guages and  sciences,  357-358;  also 
232-233.  238. 

Juliet,  Romeo  and,  87. 

Jupiter,  its  satellites  employed  in  the 
determination  of  the  velocity  of 
light,  51  et  seq. 

Jurisprudence,  Latin  and  Greek  un- 
necessary for  the  study  of,  346,  foot- 
note. 


Kant,  his  hypothesis  of  the  origin  of 
the  planetary  system,  5;  his  Critique 
of  Pure  Reason,  188 ;  on  innate  con- 
cepts of  the  understanding,  199;  on 
time,  204 :  also  footnote,  93. 

Kepler,  187,  270. 

Kinetic  energy,  177. 

Kirchhoff,  his  epistemological  ideas, 
257-258;  his  definition  of  mechan- 
ics, 236,  258,  271,  273. 

Knight,  289. 

Knowledge,  a  product  of  organic  na- 
ture, 217  et  seq.,  235 ;  instinctive, 
190;  made  possible  by  economy  of 
thought,  198 ;  our  first,  derived  from 
the  economy  of  self-preservation, 
197;  the  theory  of,  203 ;  our  primi- 
tive acts  of  the  foundation  of  sci- 
ence, 190. 

Kocher,  328. 

Koenig,  measurement  of  the  velocity 
of  sound,  57  et  seq. 

Kolliker,  19. 

Kopisch,  61. 

Kreidl,  299, 302,  306 ;  his  experiments, 
272. 

Krupp,  319. 

Labels,  the  value  of,  901. 

Labor,  the  accumulation  of,  the  foun- 
dation of  wealth  and  power,  198; 
inquirer's  division  of,  105,  258. 

Labyrinth,  of  the  ear,  18,  291,  305. 

Lactantius,  on  the  study  of  moral  and 
physical  science,  89. 

Ladder  of  our  abstraction,  the,  208. 

Ladies,  their  eyes,  71  ;  like  tuning- 
forks,  23-24. 

Lagrange,  on  Huygens's  principle, 
149;  on  the  principle  of  virtual  ve- 
locities, 150-155  ;  character  of  the 
intellectual  activity  of  m,  195,  978. 

Lake-dwellers,  46,  271. 

Lamp-shade,  70. 

Lane's  unit  jar,  115. 

Language,  knowledge  of  the  nature 
of,  demanded  by  a  liberal  educa- 
tion, 356;  relationship  between,  and 
thought,  358;  communication  by 
237;  economy  of,  191  et  seq.;  human 
its  character,  238 ;  of  animalt,  838; 


402 


INDEX. 


instruction  in,  338  et  seq.;  its  meth- 
ods, 192. 

Laplace,  on  the  atoms  of  the  brain, 
1 88  ;  on  the  scientific  achievements 
of  the  eighteenth  century,  188 ;  his 
hypothesis  of  the  origin  of  the  plan- 
etary system,  5. 

Latent  heat,  167,  178,  244. 

Latin  city  of  Maupertuis,  339. 

Latin,  instruction  in,  311  et  seq.;  in- 
troduced with  theChristianChurch, 
340;  the  language  of  scholars,  the 
medium  of  international  inter- 
course, its  power,  utility,  and  final 
abandonment,  341-347 ;  the  wealth 
of  its  literature,  348  ;  the  excessive 
study  of,  346,  349,  354,  355;  its  power 
to  sharpen  the  judgment,  357-358. 

Lavish  extravagance  of  science,  189. 

Law,  a,  defined,  256 ;  a  natural,  not 
contained  in  the  conformity  of  the 
energies,  175. 

Law-maker,  motives  of  not  always 
discernible,  9. 

Layard,  79. 

Learning,  its  nature,  366  et  seq. 

Least  superficial  area,  principle  of, 
accounted  for  by  the  mutual  attrac- 
tions of  liquid  particles,  13-14  ;  il- 
lustrated by  a  pulley  arrangement, 
12-13 ;  also  g  et  seq. 

Leibnitz,  on  harmony,  33 ;  on  inter- 
national intercourse,  342,  footnote. 

Lessing,  quotation  from,  47. 

Letters  of  the  alphabet,  their  sym- 
metry, 94,  97. 

Level  heights  of  work,  172-174. 

Lever,  a,  in  action,  222. 

Leverrier,  prediction  of  the  planet 
Neptune,  29. 

Leyden  jar,  114. 

Liberal  education,  a,  341  et  seq.,  359, 
37i. 

Libraries,  thoughts  stored  up  in,  237. 

Lichtenberg,  on  instruction,  370,  276. 

Licius,  a  Chinese  philosopher,  213. 

Liebig,  163,  278. 

Life  and  death,  186. 

Light,  history  of  as  elucidating  how 
theories  obstruct  research,  242 ; 
Huygens's  and  Newton's  views  of, 


227-228;  its  different  conceptions, 
226;  rectilinear  propagation  of,  194 ; 
role  of,  in  vision,  81 ;  spatial  and 
temporal  periodicity  of,  explains 
optical  phenomena,  194  ;  numerical 
velocity  of,  58 ;  where  does  it  go  to? 
199  ;  generally,  48  et  seq. 

Like  effects  in  like  circumstances,  199 

Likeness,  388,  391. 

Lilliput,  84. 

Lines,  straight,  their  symmetry,  98; 
curved,  their  asymmetry,  98 ;  of 
force,  249. 

Links  of  thought,  intermediate,  198 

Liquefaction,  latent  heat  of,  178. 

Liquid,  efflux,  law  of,  150 ;  equilib- 
rium, figures  of,  4  et  seq.;  the  latter 
produced  in  open  air,  7-8  ;  their 
beauty  and  multiplicity  of  form,  7, 
8 ;  made  permanent  by  melted  colo- 
phonium,  7. 

Liquids,  forms  of,  1-16;  difference 
between,  and  solids,  2 ;  their  mobil- 
ity and  adaptiveness  of  form,  3  ;  the 
courtiers  par  excellence  of  the  nat- 
ural bodies,  3  ;  possess  under  cer- 
tain circumstances  forms  of  their 
own,  3. 

Living  force,  "137, 184  ;  law  of  the  con- 
servation of,  149. 

Lloyd,  observation  of  the  conical  re- 
fraction of  light,  29. 

Lobster,  of  Lake  Mohrin,  the,  61. 

Localisation,  cerebral,  210. 

Locke,  on  language  and  thought,  358. 

Locomotive,  steam  in  the  boiler  of, 
219. 

Loeb,  J.,  289,  291,  302. 

Logarithms,  195,  219;  in  music,  103- 
104. 

Logical  root,  of  the  principle  of  en- 
ergy, 181 ;  of  the  principle  of  ex- 
cluded perpetual  motion,  182. 

Lombroso,  280. 

Lucian,  347. 

Macula  acusttca,  272. 
Magic  lantern,  96. 
Magic  powers  of  nature,  189. 
Magical  power  of  science,  belief  in 
the,  189. 


INDEX. 


4°3 


Magnet,  a,  220;  will  compared  to  the 
pressure  of  a,  14 ;  coercive  force  of 
a,  216. 

Magnetic  needle,  near  a  current,  207. 

Magnetised  bar  of  steel,  242-243. 

Major  and  minor  keys  in  music,  100 
et  seq. 

Malus,  242. 

Man,  a  fragment  of  nature's  life,  49 ; 
his  life  embraces  others,  234. 

Mann,  364. 

Manuscript  in  a  mirror,  93. 

Maple  syrup,  statues  of,  on  Moon,  4. 

Marx,  35. 

Material,  the  relations  of  work  with 
heat  and  the  consumption  of,  245 
et  seq. 

Mathematical  methods,  their  charac- 
ter, 197-198. 

Mathematics,  economy  of,  195 ;  on 
instruction  in,  338-374;  C.  G.  J. 
Jacobi  on,  280. 

Matter,  constancy  of,  203  ;  its  nature, 
203  ;  the  notion  of,  213. 

Maupertuis,  his  Latin  city,  338. 

Maximal  and  minimal  problems, their 
rftle  in  physics,  14,  footnote. 

Mayer,  J.  R.,  his  conception  of  en- 
ergy, 245,  246 ;  his  methods  of 
thought,  247 ;  on  the  conservation 
of  energy,  163, 164,  165,  167,  183,  184; 
his  metaphysical  utterances,  183 ; 
246;  also  138,  184,  191,  217,  271,  274. 

Measurement,  definition  of,  206. 

Measures,  international,  108. 

Mecanique  celeste,  90,  188 ;  sociale, 
and  morale,  the,  90. 

Mechanical,  conception  of  the  world, 
105,  155  et  seq.,  188,  207;  energy,  W. 
Thomson  on  waste  of,  175;  analo- 
gies between and  thermal  en- 
ergy, 17  et  seq.;  equivalent  of  heat, 
electricity,  etc.,  164,  167  et  seq.; 
mythology,  207;  phenomena,  physi- 
cal events  as,  182;  philosophy,  188; 
physics,  155-160,  212;  substitution- 
value  of  heat,  178,  footnote. 

Mechanics,  Kirchhoff's  definition  of, 
236. 

Medicine,  students  of,  326. 

Melody,  101. 


Melsens,  310,  327. 

Memory,  a  treasure-house  for  com- 
parison, 230,  common  elements  im- 
pressed upon  the,  180;  its  impor- 
tance, 238 ;  science  disburdens  the, 
193- 

Mendelejeff,  his  periodical  series, 
256. 

Mental,  adaptation,  214-235  ;  comple- 
tion of  phenomena,  220;  imagery, 
253;  imitation,  our  schematic,  199; 
processes,  economical,  195 ;  repro- 
duction, 198 ;  visualisation,  250. 

Mephistopheles,  88. 

Mercantile  principle,  a  miserly,  at 
the  basis  of  science,  15. 

Mersenne,  377. 

Mesmerism,  the  mental  state  of  ordi- 
nary minds,  228. 

Metaphysical  establishment  of  the 
doctrine  of  energy,  183. 

Metaphysical  spooks,  212. 

Metrical,  concepts  of  electricity,  107 
et  seq.;  notions,  energy  and  entropy 
are,  178 ;  units,  the  building-stones 
of  the  physicist,  253. 

Metronomes,  41. 

Meyer,  Lothar,  his  periodical  series 
256. 

Middle  Ages,  243,  349- 

Midsummer  Night's  Dream,  309. 

Mill,  John  Stuart.  230. 

Millers,  school  for,  326. 

Mill-wheel,  doing  work,  161. 

Mimicking  facts  in  thought,  189,  193 

Minor  and  major  keys  in  music,  100 
et  seq. 

Mirror,  symmetrical  reversion  of  ob- 
jects in,  92  et  seq. 

Miserly  mercantile  principle  at  the 
basis  of  science,  15. 

Moat,  child  looking  into,  208. 

Modern  scientists,  adherents  of  the 
mechanical  philosophy,  188. 

Molecular  theories,  104. 

Molecules,  203,  207. 

Moliere,  234. 

Momentum,  184. 

Monocular  vision,  98. 

Monotheism  of  the  Christians  and 
Jews,  187. 


INDEX. 


Montagues  and  Capulets,  87, 

Moon,  eclipse  of,  219;  lightness  of 
bodies  on,  4 ;  the  study  of  the,  90, 
284. 

Moreau,  307. 

Mosaic  of  thought,  192. 

Motion,  a  perpetual,  181 ;  quantity  of, 
184 ;  the  Eleatics  on,  158 ;  Wundt 
on,  158;  the  Herbartians  on,  158. 

Motions,  natural  and  violent,  226 ; 
their  familiar  character,  157. 

Mountains  of  the  earth,  would  crum- 
ble if  very  large,  3  ;  weight  of  bod- 
ies on,  112. 

Mozart,  44,  279. 

Miiller,  Johann,  291. 

Multiplication-table,  195. 

Multiplier,  132. 

Music,  band  of,  its  tempo  accelerated 
and  retarded,  53 ;  the  principle  of 
repetition  in,  99  et  seq.;  its  nota- 
tion,mathematicallyillustrated,io3- 
104. 

Musical  notes,  reversion  of,  101  et 
seq.;  their  economy,  192. 

Musical  scale,  a  species  of  one-di- 
mensional space,  105. 

Mystery,  in  physics,  222 ;  science  can 
dispense  with,  189. 

Mysticism,  numerical,  33 ;  in  the  prin- 
ciple of  energy,  184. 

Mythology,  the  mechanical,  of  phi- 
losophy, 207. 

Nagel,  von,  364. 

Nansen,  296. 

Napoleon,  picture  representing  the 
tomb  of,  36. 

Nations,  intercourse  and  ideas  of, 
336-337- 

Natural  constants,  193. 

Natural  law,  a,  not  contained  in  the 
conformity  of  the  energies,  175. 

Natural  laws,  abridged  descriptions, 
193;  likened  to  type,  193. 

Natural  motions,  225. 

Natural  selection  in  scientific  theo- 
ries, 63,  218. 

Nature,  experience  the  well-spring  of 
all  knowledge  of,  181 ;  fashions  of, 
64 ;  first  knowledge  of,  instinctive, 


189 ;  general  interconnexion  of,  182; 
has  many  sides,  217;  her  forces 
compared  to  purposes,  14-15 ;  lik- 
ened to  a  good  man  of  business,  15; 
the  economy  of  her  actions,  15  ;  how 
she  appears  to  other  animals,  83  et 
seq.;  inquiry  of,  viewed  as  a  tor- 
ture, 48-49 ;  view  of,  as  something 
designedly  concealed  from  man,  49; 
like  a  covetous  tailor,  9-10;  magic 
powers  of,  189 ;  our  view  of,  modi- 
fied by  binocular  vision,  82  ;  the  ex- 
perimental method  a  questioning 
of,  48. 

Negro  hamlet,  the  science  of  a,  237 

Neptune,  prediction  and  discovery  of 
the  planet,  29. 

New  views,  296  et  see}. 

Newton,  describes  polarisation,  242; 
expresses  his  wealth  of  thought  in 
Latin,  341 ;  his  discovery  of  gravita 
tion,  225  et  seq.;  his  solution  of  dis- 
persion, 362  ;  his  principle  of  the 
equality  of  pressure  and  counter- 
pressure,  191 ;  his  view  of  light,  227- 
228 ;  on  absolute  time,  204 ;  selec- 
tions from  his  works  for  use  in  in- 
struction, 368 ;  also  270,  274,  279 


Nobility,  they  displace  Latin,  342. 

Notation,  musical,  mathematically  il- 
lustrated, 103-104. 

Numbers,  economy  of,  195  ;  their  con- 
nexion with  consonance,  32. 

Numerical  mysticism,  33. 

Nursery,  the  questions  of  the,  199. 

Observation,  310. 

Observation,  in  science,  261. 

Ocean-stream,  272. 

Oettingen,  Von,  103. 

Ohm,  on  electric  currents,  249. 

Ohm,  the  word,  343. 

Oil,  alcohol,  water,  and,  employed  in 
Plateau's  experiments,  4;  free  mass 
of,  assumes  the  shape  of  a  sphere 
12;  geometrical  figures  of,  5  et  seq 

One-eyed  people,  vision  of,  98. 

Ophthalmoscope,  18. 

Optic  nerves,  96. 

Optimism  and  pessimism,  234. 


INDEX. 


405 


Order  of  physics,  197. 

Organ,  bellows  of  an,  135. 

Organic  nature,  results  of  Darwin's 

studies  of,  215  et  seq.    See  Adapta- 

tation  and  Heredity. 
Oriental  world  of  fables,  273. 
Orientation,  sensations  of,  282  et  seq. 
Oscillation,  centre  of,  147  et  seq. 
Ostwald,  172. 
Otoliths,  301  et  seq. 
Overtones,  28,  40,  349. 
Ozone,  Schobein's  discovery  of,  271. 

Painted  things,  the  difference  be- 
tween real  and,  68. 

Palestrina,  44. 

Parameter,  257. 

Partial  tones,  390. 

Particles,  smallest,  104. 

Pascheles,  Dr.  W.,  285. 

Paulsen,  338,  340,  373. 

Pearls  of  life,  strung  on  the  individ- 
ual as  on  a  thread,  234-235. 

Pencil  surpasses  the  mathematician 
in  intelligence,  196. 

Pendulum,  motion  of  a,  144  et  seq., 
increased  motion  of,  due  to  slight 
impulses,  21 ;  electrical,  no. 

Percepts,  of  like  form,  390. 

Periodical,  changes,  181 ;  series,  256. 

Permanent,  changes,  181,  199;  ele- 
ments of  the  world,  194. 

Perpetual  motion,  a,  181 ;  denned, 
139;  impossibility  of,  139  et  seq.; 
the  principle  of  the,  excluded,  140 
et  seq. ;  excluded  from  general 
physics,  162. 

Personality,  its  nature,  234-235. 

Perspective  76  et  seq.;  contraction 
of,  74  et  seq.;  distortion  of,  77. 

Pessimism  and  optimism,  234. 

Pharaohs,  85. 

Phenomenology,  a  universal  physi- 
cal, 250. 

Philistine,  modes  of  thought  of,  223. 

Philology,  comparison  in,  239. 

Philosopher,  an  ancient,  on  the  moral 
and  physical  sciences,  89. 

Philosophy,  its  character  at  all  times, 
186;  mechanical,  155  et  seq.,  188, 
207,  259  et  seq. 


Phonetic  alphabets,  their  economy 
192. 

Photography,  by  the  electric  spark 
318  et  seq. 

Photography  of  projectiles,  309-337. 

Photography,  stupendous  advances 
of,  74. 

Physical,  concepts,  fetishism  in  our 
187 ;  ideas  and  principles,  their  na- 
ture, 204 ;  inquiry,  the  economical 
nature  of,  186 ;  research,  object  of 
207,  209. 

Physical  phenomena,  as  mechanical 
phenomena,  182;  relations  between 
205. 

Physico-mechanical  view  of  the 
world,  187,  188,  207,  155  et  seq. 

Physics,  compared  to  a  well-kept 
household,  197;  economical  expe 
rience,  197;  the  principles  of,  de- 
scriptive, 199;  the  methods  of,  209; 
its  method  characterised,  an;  com- 
parison in,  239;  the  facts  of,  quali- 
tatively homogeneous,  255 ;  bow  it 
began,  37;  helped  by  psychology 
104 ;  study  of  its  own  character 
189 ;  the  goal  of,  207,  209. 

Physiological  psychology,  its  meth- 
ods, 2ii  et  seq. 

Physiology,  its  scope,  212. 

Piano,  its  mirrored  counterpart,  100 
et  seq.;  used  to  illustrate  the  facts 
of  sympathetic  vibration,  25  et  seq 

Piano-player,  a  speaker  compared  to 
192. 

Picture,  physical,  a,  no. 

Pike,  learns  by  experience,  267. 

Pillars  of  Corti,  19. 

Places,  heavy  bodies  seek  their,  224 
et  seq. 

Planetary  system,  origin  of,  illut- 
trated,  5. 

Plasticity  of  organic  nature,  216. 

Plateau,  his  law  of  free  liquid  equi- 
librium, 9 ;  his  method  of  getting 
rid  of  the  effects  of  gravity,  4- 

Plates  of  oil,  thin,  6. 

Plato,  347.  37'- 

Plautus,  347. 

Playfair,  138. 

Pleasant  effect*,  cause  of,  94  et  «eq. 


4o6 


INDEX. 


i'liny,  349. 
Poetry  and  science,  30,  31,  351. 

pared  to,  14-15  ;  nature  pursues  no 

Poinsot,  on  the  foundations  of  me- 

66. 

chanics,  152  et  seq. 

Puzzle-lock,  a,  26. 

Polarisation,  91;  abstractly  described 

Puzzles,  277. 

by  Newton,  242. 

Pyramid  of  oil,  6. 

Politics,  Chinese  speak  with  unwil- 

Pythagoras, his  discovery  of  the  laws 

lingness  of,  374. 

of  harmony,  32,  259. 

Pollak,  299. 

Polyp  plant,  humanity  likened  to  a, 

Quality  of  tones,  36. 

235- 

Quantitative  investigation,  the  goal 

Pompeii,  234  ;  art  in,  80. 

of,  180. 

Popper  J.,  172,  216. 

Quantity  of  electricity,  in,  118,  119 

et  seq.;  measurement  of,  126;  fall 

*74>  177i  244  ;  of  motion,  184. 

of,  177;   swarm  of  notions  in  the 

Quests  made  of  the  inquirer,  not  by 

idea  of,  197;  its  wide  scope,  250. 

him,  30. 

Pottery,  invention  of,  263. 

Que'telet,  15,  footnote. 

Prediction,  221  et  seq. 

Prejudice,  the  function,  power,  and 

Rabelais,  283. 

dangers  of,  232-233. 

Raindrop,  form  of,  3. 

Preparatory  schools,  the  defects  of 

Rameau,  34. 

the   German,  346-347  ;    what  they 

Reaction  and  action,  principle  of,  191 

should  teach,  364  et  seq. 

Reactions,  disclosure  of  the  connex 

Pressure  of  a  stone  or  of  a  magnet, 

ion  of,  270  et  seq. 

will  compared  to,  14;  also  157. 

Realgymnasien,  365. 

Primitive  acts  of  knowledge  the  foun- 

Realschulen, 365,  373. 

dation  of  scientific  thought,  190. 

Reason,  stands  above  the  senses,  105 

Problem,  nature  of  a,  223. 
Problems  which  are  wrongly  formu- 

Reflexion, produces  symmetrical  re- 

lated, 308. 

version  of  objects,  93  et  seq. 

Process,  Carnot's,  161  et  seq 

Refraction,  29,  193,  194,  208,  230,  231. 

Projectiles,  the  effects  of  the  impact 

Reger,  328. 

of,  310,  327-328  ;  seen  with  the  naked 

Reliefs,  photographs  of,  68. 

eye,  311,  317;  measuring  the  velo- 

Repetition, its  rOle  in  aesthetics,  89 

city  of,  332;  photography  of,  309- 

footnote,  91  et  seq.,  97,  98  et  seq.; 

337- 

390. 

Prony's  brake,  132. 

Reproduction  of  facts  in  thought,  189 

Proof,  nature  of,  284. 

193,  198,  253. 

Prophesying  events,  220  et  seq. 

Repulsion,  electric,  109  et  seq.,  168. 

Psalms,  quotation  from  the,  89. 

Research,  function  of  experimental 

Pseudoscope,  Wheatstone's,  96. 

181  ;  the  aim  of,  205. 

Psychology,  preceded  by  astronomy, 

Resemblances  between  facts,  255. 

90;  how  reached,  91  et  seq.;  helps 

Resin,  solution  of,  7. 

physical  science,  104  ;   its  method 

Resistance,  laws  of,  for  bodies  travel 

the  same  as  that  of  physics,  207  et 

ling  in  air  and  fluids,  333  et  seq. 

seq. 

Resonance,  corporeal,  392. 

Pully  arrangement,  illustrating  prin- 

Response of  sonorous  bodies,  25. 

ciple  of  least  superficial  area,  12- 

Retina,  the  corresponding  spots  of 

13- 

98  ;  nerves  of  compared  to  fingers 

Purkinje,  284,  285,  291,  299. 

of  a  hand,  96  et  seq. 

INDEX. 


407 


Reversible  processes,  161  et  seq.,  175, 

176,  181, 182. 
Rhine,  the,  94. 
Richard  the  Third,  77. 
Riddles,  277. 
Riders,  379. 
Riegler,  319. 
Riess,  experiment  with  the  thermo- 

electrometer,  133  et  seq.,  169. 
Rigid  connexions,  142. 
Rind  of  a  fruit,  190. 
Rings  of  oil,  illustrating  formation  of 

rings  of  Saturn,  5. 
Ritter,  291,  299. 
Rods  of  Corti,  19. 
Rolph,  W.  H.,  216. 
Roman    Church,    Latin    introduced 

with  the,  340  et  seq. 
Romans,  their  provinciality  and  nar- 
row-mindedness, 270. 
Romeo  and  Juliet,  87. 
Rbmer,  Olaf,  51  et  seq. 
Roots,  the  nature  of,  in  language,  252. 
Rosetti,  his  experiment  on  the  work 

required  to  develop  electricity,  131. 
Rotating  bodies,  285. 
Rotation,  apparatus  of,  in  physics,  59 

et  seq.;  sensations  of,  288  et  seq. 
Rousseau,  336. 
Rubber     pyramid,    illustrating    the 

principle  of  least  superficial  area, 

IO-II. 

Ruysdael,  279. 

Sachs,  Hans,  106. 

Salcher,  Prof.  319. 

Salviati,  144. 

Saturn,  rings  of,  their  formation  il- 
lustrated, 5. 

Saurians,  257. 

Sauveur,  on  acoustics,  34,  375  et  seq. 

Savage,  modes  of  conception  and  in- 
terpretation of  a,  218  et  seq. 

Schafer,  K.,  298. 

SchlierenmetkoJt,  317. 

Schttnbein's  discovery  of  ozone,  271. 

School-boy,  copy-book  of,  92. 

Schoolmen,  214. 

Schools,  State-control  of,  372  et  seq. 

Schopenhauer,  190. 

Schultze,  Max,  19. 


Science,  a  miserly  mercantile  princi- 
ple at  its  basis,  15  ;  compared  to  a 
business,  16 ;  viewed  as  a  maximum 
or  minimum  problem,  16,  footnote; 
its  process  not  greatly  different 
from  the  intellectual  activity  of  or- 
dinary life,  16,  footnote;  economy 
of  its  task,  16;  relation  of,  to  poetry, 
30,  31,  351;  the  church  of,  67;  be- 
ginnings of,  189,  191 ;  belief  in  the 
magical  power  of,  189;  can  dispense 
with  mystery,  189 ;  lavish  extrava- 
gance of,  189 ;  economy  of  the  ter- 
minology of,  192 ;  partly  made  up 
of  the  intelligence  of  others,  196; 
stripped  of  mystery,  197;  its  true 
power,  197 ;  the  economical  schem- 
atism of,  206;  the  object  of,  206; 
the  tools  of,  207 ;  does  not  create 
facts,  211 ;  of  the  future,  213 ;  revo 
lution  in,  dating  from  Galileo,  214 
ct  seq.;  the  natural  foe  of  the  mar- 
vellous, 224;  characterised,  227; 
growth  of,  237 ;  dramatic  element 
in,  243 ;  described,  251 ;  its  function 
253;  classification  in,  255,  259  et 
seq.;  the  way  of  discovery  in,  316. 
See  also  Physics. 

Sciences,  partition  of  the,  86;  the 
barriers  and  relations  between  the 
257-258;  on  instruction  in  the,  338- 

374- 

Scientific,  criticism,  Socrates  the 
father  of,  i,  16;  discoveries,  their 
fate,  138;  knowledge,  involves  de- 
scription, 193;  thought,  transforma- 
tion and  adaptation  in,  214-235; 
thought,  advanced  by  new  experi- 
ences, 223  et  seq.;  thought,  the  dif- 
ficulty of,  366;  terms,  34*-343I 
founded  on  primitive  acts  of  knowl- 
edge, 190. 

Scientists,  stories  about  their  ignor- 
ance, 342. 

Screw,  the,  62. 

Sea-sickness,  284. 

Secret  computation,  Leibnitz's,  33. 

Seek  their  places,  bodies,  226. 

Self- induction,  coefficient  of,  250,  252 

Self-observation,  211. 

Self-preservation,  our  first  knowledge 


4o8 


INDEX. 


derived  from  the  economy  of,  197; 
struggle  for,  among  ideas,  228. 

Semi-circular  canals,  290  et  seq. 

Sensation  of  rounding  a  railway 
curve,  286. 

Sensations,  analysed,  251 ;  when  sim- 
ilar, produce  agreeable  effects,  96 ; 
their  character,  200 ;  defined,  209 ; 
of  orientation,  282  et  seq. 

Sense-elements,  179. 

Senses,  theory  of,  104 ;  the  source  of 
our  knowledge  of  facts,  237. 

Seventh,  the  troublesome,  46. 

Shadow  method,  313  et  seq.,  317  foot- 
note. 

Shadows,  role  of,  in  vision,  81. 

Shakespeare,  278. 

Sharps,  reversed  into  flats,  101. 

Shell,  spherical,  law  of  attraction  for 
a,  124,  footnote. 

Shoemaker,  inquirer  compared  to, 
105-106. 

Shooting,  309. 

Shots,  double  report  of,  229  et  seq. 

Similarity,  249. 

Simony,  280. 

Simplicity,  a  varying  element  in  de- 
scription, 254. 

Sines,  law  of  the,  193. 

Sinking  of  heavy  bodies,  222. 

Sixth  sense,  297. 

Smith,  R.,  on  acoustics,  34,  381,  383. 

Soap-films,  Van  der  Mensbruggbe's 
experiment  with,  11-12. 

Soapsuds,  films  and  figures  of,  7. 

Social  potential,  15. 

Socrates,  the  father  of  scientific  crit- 
icism, i,  16. 

Sodium,  202. 

Sodium-light, vibrations  of.as  a  meas- 
ure of  time,  205. 

Solidity,  conception  of,  by  the  eye,  71 
et  seq.;  spatial,  photographs  of,  73. 

Solids,  and  liquids,  their  difference 
merely  one  of  degree,  2. 

Sonorous  bodies,  24  et  seq. 

Soret,  J.  P.,  89. 

Sounds,  symmetry  of,  99  et  seq.;  gen- 
erally, 22-47,  212. 

Sound-waves  rendered  visible,  315  et 


Sources  of  the  principle  of  energy,  179 
et  seq. 

Space,  205  ;  sensation  of,  210. 

Spark,  electric,  117,  127,  132,  133,  190 

Spatial  vision,  386. 

Species,  stability  of,  a  theory,  216. 

Specific  energies,  291. 

Specific  heat,  166,  244. 

Specific  inductive  capacity,  117. 

Spectral  analysis  of  sound,  27. 

Spectrum,  mental  associations  of  the 
190. 

Speech,  the  instinct  of,  cultivated  by 
languages,  354. 

Spencer,  2i8;  222. 

Sphere,  a  soft  rotating,  2 ;  the  figure 
of  least  surface,  12;  electrical  capa 
city  of,  123  et  seq. 

Spherical  shell,  law  of  attraction  for 
124,  footnote. 

Spiders,  the  eyes  of,  67. 

Spirits,  as  explanation  of  the  world 
186,  243. 

Spiritualism,  modern,  187. 

Spooks,  metaphysical,  222. 

Squinting,  72. 

Stability  of  our  environment,  206. 

Stallo,  336. 

Stars,  the  fixed,  90. 

State,  benefits  and  evils  of  its  control 
of  the  schools,  372  et  seq. ;  the 
Church  and,  88. 

Statical  electricity,  134. 

Stationary  currents,  249. 

Statoliths,  303. 

Steam-engine,  160,  265. 

Steeple-jacks,  75. 

Stereoscope,  Wheatstone  and  Brews 
ter's,  73. 

Stevinus,  on  the  inclined  plane,  140; 
on  hydrostatics,  141 ;  on  the  equi- 
librium of  systems,  142 ;  discovers 
the  principle  of  virtual  velocities 
150;  characterisation  of  his  thought 
142  ;  also  182,  187,  191. 

Stone  Age,  46,  321. 

Storensen,  306. 

Stove,  primitive,  263. 

Straight  line,  a,  its  symmetry,  98. 

Straight,  meaning  of  the  word,  240. 

Street,  vista  into  a,  75. 


INDEX. 


409 


Striae,  in  glass,  313. 

Striate  method,  for  detecting  optical 
imperfections,  317. 

Striking  distance,  115,  127. 

Strings,  vibrations  of,  249. 

Struggle  for  existence  among  ideas, 
217. 

Substance,  beat  conceived  as  a,  177, 
243  et  seq.;  electricity  as  a,  170;  the 
source  of  our  notion  of,  199 ;  r61e  of 
the  notion  of,  203,  244  et  seq.;  en- 
ergy conceived  as  a,  164,  185,  244  et 
seq. 

Substitution-value  of  heat,  178,  foot- 
note. 

Suetonius,  348. 

Sulphur,  specific  inductive  capacity 
of,  117. 

Sun,  human  beings  could  not  exist 
on,  3. 

Swift,  84,  280. 

Swimmer,  Ampere's,  207. 

Symmetry,  definition  of,  92 ;  figures 
of,  92  et  seq.;  plane  of,  94  ;  vertical 
and  horizontal,  94  ;  in  music,  99  et 
seq. 

Sympathetic  vibration,  22  et  seq.,  379. 

Tailor,  nature  like  a  covetous,  9-10. 

Tangent,  the  word,  263. 

Taste,  doubtful  cultivation  of,  by  the 
classics,  352-353  ;  of  the  ancients, 
353- 

Taylor,  on  the  vibration  of  strings, 
249- 

Teaching,  its  nature,  366  et  seq. 

Telegraph,  the  word,  263. 

Telescope,  262. 

Telestereoscope,  the,  84. 

Temperament,  even,  in  tuning,  47. 

Temperature,  absolute,  162 ;  differ- 
ences of,  205  ;  differences  of,  viewed 
as  level  surfaces,  161 ;  heights  of 
174  ;  scale  of,  derived  from  tensions 
of  gases,  174. 

Terence,  347. 

Terms,  scientific,  342-343. 

Thales,  259. 

Theories,  their  scope,  function,  and 
power,  241-242  ;  must  be  replaced 
by  direct  description,  248. 


Thermal,  energy,  174,  177 ;  capacity 
123,  footnote. 

Thermodynamics,  160  et  seq. 

Thermoelectrometer,  Riess's,  133,169 

Thing-in-itself,  the,  200. 

Things,  mental  symbols  for  groups  of 
sensations,  200-201. 

Thomson,  James,  on  the  lowering  of 
the  freezing-point  of  water  by  pres- 
sure, 162. 

Thomson,  W.,  his  absolute  electro- 
meter, 127,  footnote ;  on  thermody- 
namics, 162 ;  on  the  conservation 
of  energy,  165 ;  on  the  mechanical 
measures  of  temperature,  174,  foot- 
note ;  on  waste  of  mechanical  en- 
ergy, 175 ;  also  108,  173,  footnote. 

Thought,  habitudes  of,  199,  224,  227, 
232  ;  relationship  between  language 
and,  329 ;  incongruence  between  ex- 
perience and,  206 ;  luxuriance  of  a 
fully  developed,  58  ;  transformation 
in  scientific,  214-235. 

Thoughts,  their  development  and  the 
struggle  for  existence  among  them, 
63  ;  importance  of  erroneous,  65  ;  at 
reproductions  of  facts,  107. 

Thread,  the  individual  a,  on  whicl 
pearls  are  strung,  234-235. 

Tides,  283. 

Timbre,  37,  38,  39- 

Time,  178,  204,  205,  footnote. 

Toepler  and  Foucault,  method  of,  foi 
detecting  optical  faults,  313  et  seq. 
320. 

Tone-figures,  91. 

Tones,  22-47,  99  et  seq.,  212. 

Torsion,  moment  of,  132. 

Torsion-balance,  Coulomb's,  109, 168 

Torricelli,  on  virtual  velocities,  150; 
his  law  of  liquid  efflux,  150;  on  the 
atmosphere,  273. 

Tourist,  journey  of,  work  of  the  in- 
quirer compared  to,  17,  29,  30. 

Transatlantic  cable,  108. 

Transformation  and  adaptation  in 
scientific  thought,  214-233. 

Transformation  of  ideas,  63. 

Transformative  law  of  the  energies 
172. 

Translation,  difficulties  of,  354. 


4io 


INDEX. 


Tree,  conceptual  life  compared  to  a, 
231. 

Triangle,  mutual  dependence  of  the 
sides  and  angles  of  a,  179. 

Triple  accord,  46. 

Truth,  wooed  by  the  inquirer,  45  ;  dif- 
ficulty of  its  acquisition,  46. 

Tumblers,  resounding,  23. 

Tuning-forks,  explanation  of  their 
motion,  22  et  seq. 

Tylor,  186. 

Tympanum,  18. 

Type,  natural  laws  likened  to,  193 ; 
words  compared  to,  191. 

Ulysses,  347. 

Understanding,  what  it  means,  211. 

Uniforms,  do  not  fit  heads,  369. 

Unique  determination,  181-182. 

Unison,  43. 

Unit,  electrostatic,   in.     See   Force 

and  Work. 
United  States,  336. 
Universal  Real  Character,  a,  192. 
Utility  of  physical  science,  351. 

Variation,  the  method  of,  in  science, 
230 ;  in  biology,  216. 

Velocity,  of  light,  48  et  seq.;  of  the  de- 
scent of  bodies,  143  et  seq.;  mean- 
ing of,  204 ;  virtual,  149-155. 

Verstandesbegriffe,  199. 

Vertical,  perception  of  the,  272,  286 
etseq.;  symmetry,  389. 

Vertigo,  285,  290. 

Vestibule  of  the  ear,  300. 

Vibration,  22  et  seq. 

Vibration-figures,  91. 

Vinci,  Leonardo  da,  278,  283. 

Violent  motions,  225. 

Virtual  velocities,  149-155. 

Visibility,  general  conditions  of,  312. 

Vision,  symmetry  of  our  apparatus 
of,  96.  See  Eye. 

Visual  nerves,  96. 

Visualisation,  mental,  250. 

Volt,  the  word,  343. 

Volta,  127,  footnote,  134. 

Voltaire,  260. 

Voltaire's  ingtnu,  219. 


Vowels,  composed  of  simple  musica 
notes,  26. 

Wagner,  Richard,  279. 

Wald,  F.,  178,  footnote. 

Wallace,  216. 

War,  and  peace,  reflexions  upon,  309 

335  et  seq. 
Waste   of  mechanical  energy,  W. 

Thomson  on,  175. 
Watches,  experiment  with,  41 ;  in  a 

mirror,  93. 
Water,  jet  of,  resolved  into  drops,  60; 

free,  solid  figures  of,  8  ;  objects  re 

fleeted  in,  94,  191 ;  possible  modes 

of  measurement  of,  170. 
Watt,  266. 

Wealth,  the  foundation  of,  198. 
Weapons,  modern,  335. 
Weber,  108,  306. 
Weight  of  bodies,  varies  with  their 

distance   from   the   centre  of   the 

earth,  112. 
Weismann,  216. 
Wheatstone,  his  stereoscope,  73 ;  his 

pseudoscope,  96 ;  also  59. 
Wheel,  history  and  importance  of,  61 

et  seq. 
Whewell.on  the  formation  of  science 

231. 

Whole,  the,  204,  footnote. 
Why,  the  question,  199,  223. 
Will,  Schopenhauer  on  the, 190;  man's 

most  familiar  source  of  power,  243; 

used  to  explain  the  world,  186;  forces 

compared  to,  254;  compared  to  pres 

sure,  14. 

Windmill,  a  rotating,  53. 
Wire  frames  and  nets,  for  construct- 
ing liquid  figures  of  equilibrium,  4 

et  seq. 

Witchcraft,  187. 
Wollaston,  284,  285. 
Wonderful,  science  the  natural  foe  of 

the,  224. 
Woods,  the  relative  distance  of  trees 

in,  68. 

Wooer,  inquirer  compared  to  a,  45. 
Words  and  sounds,  343. 
Words,  compared  to  type,  191. 
Work,  of  liquid  forces  of  attraction, 


INDEX. 


411 


14;  in  electricity,  173 ;  measure  of, 
119  et  seq.,  130,  223;  relation  of,  with 
beat,  162,  245  et  seq. ;  amount  re- 
quired to  develop  electricity,  131  et 
seq. ;  produces  various  physical 
changes,  139;  substantial  concep- 
tion of,  183-184.  See  Energy. 

World,  the,  what  it  consists  of,  208. 

World-particles,  203. 

Wronsky,  172. 


Wundt,  on  causality  and  the  axioms 
of  physics,  157-159;  359  footnote. 

Xenophon,  49,  footnote. 
Young,  Thomas,  on  energy,  173. 

Zelter,  35. 

Zeuner,  171. 

Zoology,  comparison  in,  239. 


TH*  WORKS  OF  ERNST  MACH. 

THE   SCIENCE   OF  MECHANICS. 

A  CRITICAL  AND  HISTORICAL  EXPOSITION  OF  ITS 
PRINCIPLES. 

By  DR.  ERNST  MACH. 

PROFESSOR  OF  THE  HISTORY  AND  THEORY  OF  INDUCTIVE  SCIENCE  IN  THE 
UNIVERSITY  OF  VIENNA. 

Translated  from  the  Second  German  Edition 
By  THOMAS  J.  McCORMACK. 


250  Cuts.  534  Pages.  Half  Morocco,  Gilt  Top,  Marginal  Analyses. 
Exhaustive  Index.    Price  $2.50. 


TABLE  OP  CONTENT3. 

STATICS. 

The  Lever.  Virtual  Velocities. 

The  Inclined  Plane.  Statics  in  Their  Application  to  Fluids 

The  Composition  of  Forces.  Statics  in  Their  Application  to  Gases. 

DYNAMICS. 

Galileo' a  Achievements.  Newton1  s  Views  of  Time,  Space,  and 

Achievements  of  Huygens.  Motion. 

Achievements  of  Newton.  Critique  of  the  Newtonian  Enuncia- 

Principle  of  Reaction.  tions. 

Criticism  of  the  Principle  of  Reac-  Retrospect  of  the  Development  of 

tion  and  of  the  Concept  of  Mass.  Dynamics. 

THE  EXTENSION  OF  THE  PRINCIPLES  OF  MECHANICS. 

Scope  of  the  Newtonian  Principles.  Principle  of  Vis  Viva. 

Formula  and  Units  of  Mechanics.  Principle  of  Least  Constraint 

Conservation  of  Momentum,  Conser-  Principle  of  Least  Action. 

vation  of  the  Centre  of  Gravity,  Hamilton's  Principle. 

and  Conservation  of  Areas.  Hydrostatic  and  Hydrodynamlc 
Laws  of  Impact.  Question*. 

D'Alembert's  Principle. 

FORMAL  DEVELOPMENT  OF  MECHANICS. 

The  Isoperimetrical  Problems.  Analytical  Mechanics. 

Theological,  Animistic,  and  Mystical        The  Economy  of  Scieno*. 
Points  of  View  in  Mechanics. 

THE  RELATION  OF  MECHANICS  TO  OTHER  DEPARTMENTS  OF  KKOWI.BDOB. 
Relations  of  Mechanics  to  Physics.  Relations  of  Mechanics  to  Physioloc? 


THE  WORKS  OF  ERNST  MACh, 

PRESS  NOTICES. 

"The  appearance  of  a  translation  into  English  of  this  remarkable  book 
should  serve  to  revivify  in  this  country  [England]  the  somewhat  stagnating 
treatment  of  its  subject,  and  should  call  up  the  thoughts  which  puzzle  us  when 
we  think  of  them,  and  that  is  not  sufficiently  often.  .  .  .  Professor  Mach  is  a 
striking  instance  of  the  combination  of  great  mathematical  knowledge  with 
experimental  skill,  as  exemplified  not  only  by  the  elegant  illustrations  of  me- 
chanical principles  which  abound  in  this  treatise,  but  also  from  his  brilliant 
experiments  on  the  photography  of  bullets.  ...  A  careful  study  of  Professor 
Mach's  work,  and  a  treatment  with  more  experimental  illustration,  on  the 
lines  laid  down  in  the  interesting  diagrams  of  his  Science  of  Mechanics,  will 
do  much  to  revivify  theoretical  mechanical  science,  as  developed  from  the 
elements  by  rigorous  logical  treatment."— Prof.  A.  G.  Greenhill,  in  Nature, 
London. 

"  Those  who  are  curious  to  learn  how  the  principles  of  mechanics  hare 
been  evolved,  from  what  source  they  take  their  origin,  and  how  far  they  can 
be  deemed  of  positive  and  permanent  value,  will  find  Dr.  Mach's  able  trea- 
tise entrancingly  interesting.  .  .  .  The  book  is  a  remarkable  one  in  many  re- 
spects, while  the  mixture  of  history  with  the  latest  scientific  principles  and 
absolute  mathematical  deductions  makes  it  exceedingly  attractive."— Me- 
chanical World,  Manchester  and  London,  England. 

"  Mach's  Mechanics  is  unique.  It  is  not  a  text-book,  but  forms  a  useful 
supplement  to  the  ordinary  text-book.  The  latter  is  usually  a  skeleton  out- 
line, full  of  mathematical  symbols  and  other  abstractions.  Mach's  book  has 
'muscle  and  clothing,'  and  being  written  from  the  historical  standpoint,  in- 
troduces the  leading  contributors  in  succession,  tells  what  they  did  and  how 
they  did  it,  and  often  what  manner  of  men  they  were.  Thus  it  is  that  the 
pages  glow,  as  it  were,  with  a  certain  humanism,  quite  delightful  in  a  scien- 
tific book.  .  .  .  The  book  is  handsomely  printed,  and  deserves  a  warm  recep- 
tion from  all  interested  in  the  progress  of  science."— The Phytical Review,  New 
York  and  London. 

"  Mr.  T.  J.  McCormack,  by  his  effective  translation,  where  translation 
was  no  light  task,  of  this  masterly  treatise  upon  the  earliest  and  most  funda- 
mental of  the  sciences,  has  rendered  no  slight  service  to  the  English  speak- 
ing student.  Thetferman  and  English  languages  are  generally  accounted 
second  to  none  in  their  value  as  instruments  for  the  expression  of  scientific 
thought ;  but  the  conversion  bodily  of  an  abstruse  work  from  one  into  the 
other,  so  as  to  preserve  all  the  meaning  and  spirit  of  the  original  and  to  set  it 
easily  and  naturally  into  its  new  form,  is  a  task  of  the  greatest  difficulty,  and 


THE  WORKS  OF  ERNST  MACH. 

when  performed  so  well  as  in  the  present  instance,  merits  great  commenda- 
tion. Dr.  Mach  has  created  for  his  own  works  the  severest  possible  standard 
of  judgment.  To  expect  no  more  from  the  books  of  such  a  master  than  from 
the  elementary  productions  of  an  ordinary  teacher  in  the  science  would  be 
undue  moderation.  Our  author  has  lifted  what,  to  many  of  ns,  was  at  one 
time  a  course  of  seemingly  unprofitable  mental  gymnastics,  encompassed 
only  at  vast  expenditure  of  intellectual  effort,  into  a  study  possessing  a  deep 
philosophical  value  and  instinct  with  life  and  interest.  '  No  profit  grows 
where  is  no  pleasure  ta'en,'  and  the  emancipated  collegian  will  turn  with 
pleasure  from  the  narrow  methods  of  the  text-book  to  where  the  science  is 
made  to  illustrate,  by  a  treatment  at  once  broad  and  deep,  the  fundamental 
connexion  between  all  the  physical  sciences,  taken  together."—  Tin  Mining 
Journal,  London,  England. 

"As  a  history  of  mechanics,  the  work  is  admirable."— The  Natitn,  New 
York. 

"An  excellent  book,  admirably  illustrated."— The  Literary  W»rld,  Lon- 
don, England. 

"Sets  forth  the  elements  of  its  subject  with  a  lucidity,  clearness,  and 
force  unknown  in  the  mathematical  text-books  ....  is  admirably  fitted  to 
serve  students  as  an  introduction  on  historical  lines  to  the  principles  of  me- 
chanical science."— Canadian  Mining  and  Mechanical  Review,  Ottawa,  Can. 

"A  masterly  book To  any  one  who  feels  that  he  does  not  know  as 

much  as  he  ought  t*  about  physics,  we  can  commend  it  most  heartily  as  a 

scholarly    and  able  treatise both  interesting  and   profitable."— A.  M. 

Wellington,  in  Engineering  Newt,  New  York. 

"The  book  as  a  whole  is  unique,  and  is  a  valuable  addition  to  any  library 

•f  science  or  philosophy Reproductions  of   quaint  old  portraits  and 

vignettes  give  piquancy  to  the  pages.  The  numerous  marginal  title*  form  a 
complete  epitome  of  the  work;  and  there  is  that  invaluable  adjunct,  a  good 
index.  Altogether  the  publishers  are  to  be  congratulated  upon  producing  a 
technical  work  that  is  thoroughly  attractive  in  its  make-up."— Prof.  D.  W. 
Hering,  in  Science. 

"  There  is  one  other  point  upon  wftich  this  volume  should  be  commended, 
and  that  is  the  perfection  of  the  translation.  It  is  a  common  fault  that  bo»ki 
of  the  greatest  interest  and  value  in  the  original  are  ofteneit  butchered  »r 
made  ridiculous  by  a  clumsy  translator.  The  present  is  a  noteworthy  excep- 
tion. "—Railway  Aft. 


THE  WORKS  OF  ERNST  MACH. 

"The  book  is  admirably  printed  and  bound.  .  .  .  The  presswork  is  un- 
excelled by  any  technical  books  that  have  come  to  our  hands  for  some  time, 
and  the  engravings  and  figures  are  all  clearly  and  well  executed."— Railroad 
Gazette. 

TESTIMONIALS  OF  PROMINENT  EDUCATORS. 

"  I  am  delighted  with  Professor  Mach's  Science  of  Mechanic*."— M.  E. 
Cooley,  Professor  of  Mechanical  Engineering,  Ann  Arbor,  Mich. 

"You  have  done  a  good  service  to  science  in  publishing  Mach's  Science 
of  Mechanics  in  English.  I  shall  take  every  opportunity  to  recommend  it  to 
young  students  as  a  source  of  much  interesting  information  and  inspiration." 
— M.  I.  Pupin,  Professor  of  Mechanics,  Columbia  College,  New  York. 

"Mach's  Science  of  Mechanic!  is  an  admirable book."-/V^  E.  A. 

Futrtes,  Director  of  the  College  of  Civil  Engineering  of  Cornell  University, 
Ithaca,  N.  Y. 

'.'I  congratulate  you  upon  producing  the  work  in  such  good  style  and  in 
so  good  a  translation.  I  bought  a  copy  of  it  a  year  ago,  very  shortly  after  you 
issued  it.  The  book  itself  is  deserving  of  the  highest  admiration;  and  you 
are  entitled  to  the  thanks  of  all  English-speaking  physicists  for  the  publica- 
tion of  this  translation."— D.W.Hering,  Professor  of  Physics,  University  of 
the  City  of  New  York,  New  York. 

"  I  have  read  Mach's  Science  of  Mechanics  with  great  pleasure.  The  book 
is  exceedingly  interesting." — W.  F.  Magie,  Professor  of  Physics,  Princeton 
University,  Princeton,  N.  J. 

"The  Science  of  Mechanic*  by  Mach,  translated  by  T.  J.  McCormack,  I 
regard  as  a  most  valuable  work,  not  only  for  acquainting  the  student  with  the 
history  of  the  development  of  Mechanics,  but  as  serving  to  present  to  him 
most  favorably  the  fundamental  ideas  of  Mechanics  and  their  rational  con- 
nexion with  the  highest  mathematical  developments.  It  is  a  most  profitable 
book  to  read  along  with  the  study  of  a  text-book  of  Mechanics,  and  I  shall 
take  pleasure  in  recommending  its  perusal  by  my  students." — 5.  W.Robinson, 
Professor  of  Mechanical  Engineering,  Ohio  State  University,  Columbus,  Ohio. 

"  I  am  delighted  with  Mach's  '  Mechanics.'  I  will  call  the  attention  to 
it  of  students  and  instructors  who  have  the  Mechanics  or  Physics  to  study  or 
teach."—/.  E.  Davits,  University  of  Wisconsin,  Madison,  Wis. 

"There  can  be  but  one  opinion  as  to  the  value  of  Mach's  work  in  this 
translation.  No  instructor  in  physics  should  be  without  a  copy  of  it." — Henry 
Crew,  Professor  of  Physics  in  the  Northwestern  University,  Evansten,  111. 


THE  WORKS  OF  ERNST  MACH. 

POPULAR  SCIENTIFIC  LECTURES, 

A  PORTRAYAL  OF  THE  SPIRIT  AND  METHODS 
OF  SCIENCE. 

By  DR.  ERNST  MACH. 

PROFESSOR  OF  THE  HISTORY  AND  THEORY  OF  INDUCTIVE  SCIENCE  IN  THE 
UNIVERSITY  OF  VIENNA. 

Translated  by  THOMAS  J.  McCORMACK. 

Third  Edition,  Revised  Throughout  and  Greatly  Enlarged. 


Cloth,  Gilt  Top.    Exhaustively  Indexed.    Pages,  415.    Cuts,  59.    Price,  $1.50. 


TITLES  OP  THE  LECTURES. 

The  Forms  of  Liquids.  On  the  Principle  of  Comparison  in 

The  Fibres  of  Corti.  Physics. 

On  the  Causes  of  Harmony.  On  the  Part  Played  by  Accident  in 

On  the  Velocity  of  Light.  Invention  and  Discovery. 

Why  Has  Man  Two  Eyes?  On  Sensations  of  Orientation. 

On  Symmetry.  On  the  Relative  Educational  Value 

On   the    Fundamental    Concepts   of  of  the  Classics  and  the  Mathemat- 

Static  Electricity.  ico-Physical  Sciences. 

On  the  Principle  of  the  Conservation  A  Contribution   to    the    History   of 

of  Energy.  Acoustics. 

On  the  Economical  Nature  of  Phys-  Remarks  on  the  Theory  of  Spatial 

ical  Inquiry.  Vision. 

On  Transformation  and  Adaptation  in  Scientific  Thought. 

PRESS  NOTICES. 

"A  most  fascinating  volume,  treating  of  phenomena  in  which  all  are  in- 
erested,  in  a  delightful  style  and  with  wonderful  clearness.  For  lightness 
of  touch  and  yet  solid  value  of  information  the  chapter  'Why  Has  Man  Two 
Eyes? '  has  scarcely  a  rival  in  the  whole  realm  of  popular  scientific  writing." 
—  The  Boston  Traveller. 

"Truly  remarkable  in  the  insight  they  give  into  the  relationship  of  the 
various  fields  cultivated  under  the  name  of  Physics.  ...  A  vein  of  humor  is 
met  here  and  there  reminding  the  reader  of  Heaviside,  never  offending  one's 
taste.  These  features,  together  with  the  lightness  of  touch  with  which  Mr. 
McCormack  has  rendered  them,  make  the  volume  one  that  may  be  fairly 
called  rare.  The  spirit  of  the  author  is  preserved  in  such  attractive,  really 
delightful,  English  that  one  is  assured  nothing  has  been  lost  by  translation." 
—Prof.  Henry  Crew,  in  The  Attropkysical  Journal. 


THE  WORKS  OF  ERNST  MACH. 

"A  very  delightful  and  useful  book.  .  .  .  The  author  treats  some  of  the 
most  recondite  problems  of  natural  science,  in  so  charmingly  untechnical  a 
way,  with  such  a  wealth  of  bright  illustration,  as  makes  his  meaning  clear  to 
the  person  of  ordinary  intelligence  and  education.  .  .  .  This  is  a  work  that 
should  find  a  place  in  every  library,  and  that  people  should  be  encouraged  to 
read." — Daily  Picayune,  New  Orleans. 

"  In  his  translation  Mr.  McCormack  has  well  preserved  the  frank,  sim- 
ple, and  pleasing  style  of  this  famous  lecturer  on  scientific  topics.  Professor 
Mach  deals  with  the  live  facts,  the  salient  points  of  science,  and  not  with  its 
mysticism  or  dead  traditions.  He  uses  the  simplest  of  illustrations  and  ex- 
presses himself  clearly,  tersely,  and  with  a  delightful  freshness  that  makes 
entertaining  reading  of  what  in  other  hands  would  be  dull  and  prosy."— En- 
gineering Newt,  N.  Y. 

"  The  general  reader  is  led  by  plain  and  easy  steps  along  a  delightful  way 
through  what  would  be  to  him  without  such  a  help  a  complicated  maze  of 
difficulties.  Marvels  are  invented  and  science  is  revealed  as  the  natural  foe 
to  mysteries."— The  Chautauguan. 

"The  beautiful  quality  of  the  work  is  not  marred  by  abstruse  discussions 
which  would  require  a  scientist  to  fathom,  but  is  so  simple  and  so  clear  that 
it  brings  us  into  direct  contact  with  the  matter  treated." — The  Boston  Post. 

"A  masterly  exposition  of  important  scientific  truths."— Scotsman,  Edin- 
burgh. 

"  These  lectures  by  Dr.  Mach  are  delightfully  simple  and  frank  ;  there  is 
no  dryness  or  darkness  of  technicalities,  and  science  and  common  life  do  not 
seem  separated  by  a  gulf.  .  .  .  The  style  is  admirable,  and  the  whole  volume 
seems  gloriously  alive  and  human." — Providence  Journal,  R.  I. 

"  The  non-scientific  reader  who  desires  to  learn  something  of  modern 
scientific  theories,  and  the  reasons  for  their  existence,  cannot  do  better  than 
carefully  study  these  lectures.  The  English  is  excellent  throughout,  and  re- 
flects great  credit  on  the  translator." — Manufacturer  and  Builder. 

"We  like  the  quiet,  considerate  intelligence  of  these  lectures." — Inde- 
pendent, New  York. 

"  Professor  Mach's  lectures  are  so  pleasantly  written  and  illumined  with 
inch  charm  of  illustration  that  they  have  all  the  interest  of  lively  fiction." — 
New  York  Com.  Advertiser, 

"The  literary  and  philosophical  suggestiveness  of  the  book  is  very  rich." 
Hartford  Seminary  Record. 


THE  WORKS  OF  ERNST  MACH. 


"All  are  presented  so  skilfully  that  one  can  imagine  that  Professor  Mach's 
hearers  departed  from  his  lecture-room  with  the  conviction  that  science  was 
a  matter  for  abecedarians.  Will  please  those  who  find  the  fairy  tales  of 
science  more  absorbing  than  fiction."—  The  Pilot,  Boston. 

"  Professor  Mach  ...  is  a  master  in  physics.  .  .  .  His  book  is  a  good  one 
and  will  serve  a  good  purpose,  both  for  instruction  and  suggestion  " — Prof 
A.  E.  Dolbear,  in  The  Dial. 

"The  most  beautiful  ideas  are  unfolded  in  the  exposition."— Catholic 
World,  New  York. 


THE  ANALYSIS  OF  THE  SENSATIONS 


By  DR.  ERNST  MACH. 


PROFESSOR  OF  THE  HISTORY  AND  THEORY  OF  INDUCTIVE  SCIENCE  IN  THE 
UNIVERSITY  OF  VIENNA. 


Pages,  208.     Illustrations,  37.     Indexed. 
(Price,  Cloth,  $1.25.) 


CONTENTS. 

Introductory :  Antimetaphysical.  tions  to  One  Another  and  to  the 

The  Chief  Points  of  View  for  the  In-  Other  Psychical  Elements. 

vestigatioii  of  the  Senses.  The  Sensation  of  Time. 

The  Space-Sensations  of  the  Eye.  The  Sensation  of  Sound. 

Space-Sensation,  Continued.  Influence  of  the  Preceding  Investiga- 

The  Relations  of    the  Sight-Sensa-  tions  on  the  Mode  of  Conceiving 

Physics. 


"A  wonderfully  original  little  book.  Like  everything  he  writes  a  work  of 
genius." — Prof.  W.  James  of  Harvard. 

"  I  consider  each  work  of  Professor  Mach  a  distinct  acquisition  to  a 
library  of  science."— Prof.  D.  W.  Hering,  New  York  University. 

"There  is  no  work  known  to  the  writer  which,  in  its  general  scientific 
bearings,  is  more  likely  to  repay  richly  thorough  study.  We  are  all  interested 
in  nature  in  one  way  or  another,  and  pur  interests  can  only  be  heightened 
and  clarified  by  Mach's  wonderfully  original  and  wholesome  book.  It  is  not 
saying  too  much  to  maintain  that  every  intelligent  person  should  have  a  copy 
of  it, — and  should  study  that  copy." — Prof.  J.  E.  Trevor,  Cornell. 

"  Students  may  here  make  the  acquaintance  of  some  of  the  open  ques- 
tions of  sensation  and  at  the  same  time  take  a  lesson  in  the  charm  of  scien- 
tific modesty  that  can  hardly  be  excelled."— Prof.  E.  C.  San/orJ,  Clark  Uni- 
versity. 

"  It  exhibits  keen  observation  and  acute  thought,  with  many  new  and  in- 
teresting experiments  by  way  of  illustration.  Moreover,  the  style  is  light 
and  even  lively— a  rare  merit  in  a  German  prose  work,  and  still  rarer  in  a 
translation  of  one."— The  Literary  World,  London. 


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Separate  copies  according  to  prices  quoted.  The  books  are  printed  upon 
good  paper,  from  large  type. 

The  Religion  of  Science  Library,  by  its  extraordinarily  reasonable  price, 
will  place  a  large  number  of  valuable  books  within  the  reach  of  all  readers 

The  following  have  already  appeared  in  the  series  : 

No.  i.   The  Religion  of  Science.     By  PAUL  CARUS.     250. 

2.  Three  Introductory  Lectures  on  the  Science  of  Thought.     By  F.  MAX 

MOLLER.      25C. 

3.  Three  Lectures  on  the  Science  of  Language.     By  F.  MAX  MULLER.    250. 

4.  The  Diseases  of  Personality.    By  TH.  RIBOT.     250. 

5.  The  Psychology  of  Attention.     By  TH.  RIBOT.     250. 

6.  The  Psychic  Life  of  Micro-Organisms.     By  ALFRED  BINET.     250. 

7.  The  Nature  of  the  State.     By  PAUL  CARUS.     150. 

8.  On  Double  Consciousness.     By  ALFRED  BINET.     150. 

9.  Fundamental  Problems.     By  PAUL  CARUS.     500. 

10.  The  Diseases  of  the  Will.     By  TH.  RIBOT.     250.      ' 

11.  The  Origin  of  Language.     By  LUDWIG  NOIRE.     150. 

12.  The  Free  Trade  Struggle  in  England.     By  M.  M.  TRUMBULL.     250. 

13.  Wheelbarrow  on  the  Labor  Question.     By  M.  M.  TRUMBULL.     350. 

14.  The  Gospel  of  Buddha.     By  PAUL  CARUS.     350. 

15.  The  Primer  of  Philosophy.     By  PAUL  CARUS.     250. 

16.  On  Memory,  and  The  Specific  Energies  of  the  Nervous  System.    By  PROF. 

EWALD  HERING.    150. 

17.  The  Redemption  of  the  Brahman.     A  Tale  of  Hindu  Life.     By  RICHARD 

GARBE.    250. 

18.  An  Examination  of  Weismannism.     By  G.  J.  ROMANES.     350. 

19.  On  Germinal  Selection.     By  AUGUST  WEISMANN.     250. 

20.  Lovers  Three  Thousand  Years  Ago.    By  T.  A.  GOODWIN.     150. 

21.  Popular  Scientific  Lectures.     By  ERNST  MACH.     500. 

22.  Ancient  India  :  Its  Language  and  Religions.     By  H.  OLDENBERG.     250. 

23.  The  Prophets  of  Ancient  Israel.     By  PROF.  C.  H.  CORNILL.     250. 

24.  Homilies  of  Science.     By  PAUL  CARUS.     350. 

25.  Thoughts  on  Religion.     By  G.  J.  ROMANES.     50  cents. 

26.  The  Philosophy  of  Ancient  India.     By  PROF.  RICHARD  GARBE.     250. 

27.  Martin  Luther.     By  GUSTAV  FREYTAG.     250. 

28.  English  Secularism.    By  GEORGE  JACOB  HOLYOAKE.    250. 

29.  On  Orthogenesis.    By  TH.  EIMER.    250. 

30.  Chinese  Philosophy.     By  PAUL  CARUS.     250. 

31.  The  Lost  Manuscript.    By  GUSTAV  FREYTAG.    6oc. 


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time  is  the  object  of  The  Open  Court.  Thus,  the  religion  of  The  Open  Court  is 
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Court  does  not  attack  the  properly  religious  element  of  the  various  religions. 
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to  preserve  of  them  all  that  is  true  and  good. 

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of  the  day.  The  following  have  contributed  to  its  columns  : 


PROF.  JOSEPH  LE  CONTE, 
DR.  W.  T.  HARRIS, 
M.  D.  CONWAY, 
CHARLES  S.  PEIRCE, 
PROF.  F.  MAX  MOLLER, 
PROF.  E.  D.  COPE, 
CARUS  STERNE, 
MRS.  C.  LADD  FRANKLIN, 
PROF.  MAX  VERWORN, 
PROF.  FELIX  KLEIN, 

PROF.  G.  J.  ROMANES, 
PROF.  C.  LLOYD  MORGAN, 
JAMES  SULLY, 
B.  BOSANQUET, 
DR.  A.  BINET, 
PROF.  ERNST  MACH, 
RABBI  EMU.  HIRSCH, 
LESTER  F.  WARD, 
PROF.  H.  SCHUBERT, 
DR.  EDM.  MONTGOMERY, 

PROF.  C.  LOMBROSO, 
PROF.  E.  HAF.CKEL, 
PROF.  H.  HOFFDING, 
DR.  F.  OSWALD, 
PROF.  J.  DBLBOBUF, 
PROF.  F.  JODL, 
PROF.  H.  M.  STANLEY, 
G.  FERRERO, 
I.  VENN, 
PROF.  H.  VON  HOLST. 

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